It may be explored in Minions (film) which may act as a prequel or spin off to the Despicable Me franchise coming in 2015, as per the movie description in Wikipedia it states - Minions are yellow henchmen who have existed since the beginning of time, serving history's most ambitious villains.
Update:
As per then Minions (film)
Minions are small, yellow creatures who have existed since the beginning of time, evolving from single-celled organisms into beings who exist only to serve history's most despicable masters.
Note:
Copied from my own answer from Movies & TV Stackexchnage.
scifi.stackexchange.com/users/6006/Victor Salazar
The short film "Minions : Orientation Day" explains that all of the minions are
[generically] engineered from the same strand of mutated DNA.
As has been pointed out by @DaveJOhnson
this is contradicted by the latest trailer for Minions (2014) which shows the minions having existed since the time of the dinosaurs, some 200+ million years ago
scifi.stackexchange.com/users/20774/Valorum
The minions are possibly made from humans by a ray that turns humans into minions as seen in the Minions Mayhem ride at Universal Studios.
This is generally considered as non-canon (or just something Gru invented for the express purpose of the ride).
However, one of the short films (in Orientation Day) suggests they are made from a single strand of mutated DNA Reference: Despicable Me Wiki
scifi.stackexchange.com/users/16528/Ganesh Babu
No, they evolved naturally.
A description of the film explained that they arose through evolution, but is scant on the details: Minions have existed since the beginning of time.
They have evolved from single (yellow) cell organisms into the familiar beings we know.
The film’s title include small, yellow cells that gradually mutate into familiar Minion shapes.
These cells are depicted following a series of larger organisms (as they evolve), presumably assisting and abetting them in whatever it is they do.
At the end of the film, it is made clear that they were not created by Gru, because They meet and follow Gru when he steals the Queen’s crown, but have been active long before they met him.
scifi.stackexchange.com/users/3567/alexwlchan
As we see in the trailer for the new movie, they have been on the planet for millions of years.
The movie itself may or may not go into more detail, as the trailer gives the impression that the bulk of the movie has to do with how they came to work for Gru.
scifi.stackexchange.com/users/14710/Dave Johnson
Minions came from yellow single cell organisms that were created in the ocean.
Many animals originated from the ocean so it is not a surprise to see them walk out too, in the popular film Minions.
In the begging of the first film when the opening credits come on it shows how they evolve from being round cylinders to having little dangling arms and leg, then have one or two eyes with goggles, and so on until they stop at the usual normal-ish minions.
scifi.stackexchange.com/users/62753/FLUFFYUNICORNPOWER
I have recently watched the movie Despicable Me. Are Minions personally created by Dr. Gru?
Where did the Minions come from?
scifi.stackexchange.com
<movie><despicable-me>
scifi.stackexchange.com/questions/39659
scifi.stackexchange.com/users/16775/Nescient
Minions are said to have existed since the beginning of time. They evolved from single (yellow) cell organisms into the beings we now know, serving history's most ambitious villains.   The film’s title include small, yellow cells that gradually mutate into familiar Minion shapes. The minions have existed since the beginning of time from a single strand of mutated DNA. They came about as small, yellow cells from the ocean; hence they evolved naturally.
The minions have existed since the beginning of time from a single strand of mutated DNA. They came about as small, yellow cells from the ocean. The minions evolved naturally.