Assuming, that dark matter particles are "collisionless" there is very little constraint regarding particle mass.
For a "thermal freeze out" sub-type of dark matter there is a viral relationship between mass and mean-velocity of dark matter, this puts a lower and upper bound on dark matter mass from the extent of large scale structure in this scenario. But, there is no likelihood that dark matter is "thermal freeze out" dark matter.
But, in the general case there are not strong limits. Dark matter candidate papers range from candidates with 10-26 GeV and up to at least asteroid mass.