There are a lot of films with actors/actresses who dominate the film, but actually have very little screen time.
For example, Orson Welles in
The Third Man had ~10 minutes of screen time.
Heath Ledger in
The Dark Knight had just under 20 minutes.
Judi Dench won an Oscar for Shakespeare in Love for less than 8 minutes acting time.
Similarly, Beatrice Straight won an Oscar for Network , based on ~10 minutes acting time.
Anne Hathaway also won an Oscar for Les Miserables , based on ~15 minutes screen time.
Of course, the problem with all of these is that they don't fit the scope of your question - in that the actors involved, whilst highly billed, were not the highest billed.
Given this, the best answer I can think of is
The Silence of the Lambs , starring, as the joint top-billed actor, Anthony Hopkins .
He had less than 16 minutes of screen time, which is more than the others above, but at least shared the top billing.
Unfortunately, I'm not sure how to verify anything lower than this.
There are plenty of people who have had high billing despite having a mere cameo, but I'm not aware of anyone actually leading the credit listings with a lower time than this (although I'll happily amend my answer if I find anyone).
Edit : Marlon Brando in Superman received joint top billing with Gene Hackman (who played Lex Luthor).
Christopher Reeve, who played Superman, was billed much lower as he was relatively unknown at the time.
Brando has ~8 minutes of screen time , which is much less than Anthony Hopkins.
Edit 2 :
If joint top billing is to be allowed, as many have commented Mark Hamill, who shared top-billing with a host of other people, had a mere minute or two of on-screen presence in Star Wars VII: The Force Awakens .
Edit 3 :
Neither of us have confirmed this, but @Thunderforge has suggested Tobin Bell in Saw 3D, who was given solo top billing and
apparently only had two minutes of screen play.
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EDIT:
We might have a new record.
In the US historical epic One Night with the King from 2006, Peter O'Toole briefly appears in the prologue as the Prophet Samuel for "barely 30 seconds" , according to Leonard Maltin's 2015 Movie Guide .
(I timed it myself
and it's about 25 seconds).
Despite this, he's top-billed as the film's star:
Another notable example would be Ed Wood's Plan 9 From Outer Space from 1959.
It's a B-movie, but by all means not experimental or avant-garde.
It was famously filmed after Bela Lugosi's death and more or less based around some brief, silent footage of him which Wood shot before he died.
Wood originally promoted it as "Bela Lugosi's last movie", and to make Bela's role more prominent, Wood then hired his wife's chiropractor as a stand in.
So, although Lugosi's actual screen time is under 3 minutes (I counted it myself),
he's still top-billed in the original promotional art :
[However, there is also the dubious practice of retroactively displaying a famous actor prominently in the promotional art of their older, more obscure films in which they only briefly appeared.
TVTropes calls this Billing Displacement and features a few trillion examples, so you might find some more fitting titles there too.]
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Steve McQueen was the top billed actor of The Great Escape .
He has very few lines, and spends almost all his screen time throwing a baseball off a wall into his glove.
Supposedly he was slated to have even less (and was nearly thrown out of the movie entirely), but insisted on being given something "heroic" to do.
Part of the problem, it seemed, was McQueen’s determination that his character remain cool and inscrutable. '
We finally figured out,’ Garner said, '“Steve, you want to be the hero, but you don’t want to do anything heroic.”’
So a scene was added near the end of him failing to escape on a motorcycle.
But even that scene was done by a stunt-double, not McQueen himself.
I can't find a definitive number for McQueen's screen time online, nor a stream of the movie.
However, youtube has a series of 11 clips .
Adding up his screen time from all of them, it appears that he had at least 10 minutes of screen time in the movie, which works out to a bit less than 6%.
But that's a lower bound, not upper.
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There are a lot of good answers, but there is one movie that is notorious for having the top-billed actor have very little screen time.
The movie Game Of Death (1978) stars Bruce Lee, well kind of.
All you history buffs know where I am going with this.
Bruce Lee was already long dead before this movie was released.
There was tons of archive footage that wasn't being used, so the film makers decided to make an entire movie using these clips.
Unfortunately, they did not have enough footage, so they had to insert cardboard cutouts of Lee
(I kid you not)
as a stand in.
Here is a clip showing just how egregious some of these scenes are.
Cardboard Cutout Bruce
Bruce Lee is the top-billed actor in this film, yet he did not actually act in this movie.
The acting for this film that he did was technically 0 minutes.
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Alec Baldwin, Blake, 7:23 of 100:00 (7.3%), Glengarry Glen Ross, billing (third or shared first, I don't find querier has resolved in other comments):
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George Clooney, The Thin Red Line (1998)
Albeit having a huge ensemble cast, in this 2-hour 50-minute feature he has less than maybe 2 minutes of screen time.
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What is the least amount of screen time, relative to the total running length, that the single highest-billed actor (or actress) has ever had in a feature-length, non-experimental film?  (For the purposes of this question, "screen time" includes time spent doing voice-overs.)
Top-billed actor with the least screen time
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The Silence of the Lambs, One Night with the King and Game of Death and The Thin RedLine are just some of the films where a top-billed actor has very little screen time. As far as There are a lot of films with actors/actresses who dominate the film, but actually have very little screen time. 
There are a lot of films with actors/actresses who dominate the film, but actually have very little screen time.  The Silence of the Lambs, starring the joint top-billed actor, Anthony Hopkin. Steve McQueen was the top billed actor in The Great Escape. Peter O'Toole briefly appears in the prologue of One Night with the King for "barely 30 seconds" George Clooney has less than maybe 2 minutes of screen time in The Thin Red Line. The movie Game Of Death (1978) stars Bruce Lee, well kind of. Bruce Lee was already long dead before this movie was released. Alec Baldwin, Blake, 7:23 of 100:00 (7.3%).