Reid, who became the first GB woman to reach an Olympic individual 3m springboard final at Rio 2016, scored a personal best total of 336.70 from her five routines.
"I can't believe it, what just happened, I have no words," the Scottish diver told BBC Sport.
Tingmao Shi (383.50) took gold ahead of fellow Chinese diver Han Wang (359.40).
Canada's Jennifer Abel (351.55) was third.
The performance of 21-year-old Reid is all the more impressive given she has combined training with studies in applied sports science at the University of Edinburgh.
Bob Ballard, BBC Sport commentator
I suggested yesterday that Edinburgh's Grace Reid was capable of a top-six finish in the final of the women's 3m springboard and so it proved to be.
Fourth place and an improvement from the semi-final of four places and 30 points.
She's only been working with 2014 Commonwealth medallist Nick Robinson-Baker for a matter of months and the early indications of their partnership are looking fruitful.
Reid looked calm and composed on the springboard throughout and the experience of having competed at international level for seven years gives the impression she belongs in this company.
More World Series experience next year and she will be sharper still. I predict exciting times ahead for the Scot.
British 3m springboard diver Grace Reid finished an impressive fourth in her World Championship debut in Budapest.