I believe you are looking for hydrostatic equilibrium. There don’t seem to be good answers for this online, but according to Robert Black on this Quora post:

There isn’t a minimium per se but the generally accepted number for a mass to form into a sphere under its own gravity is 1/10,000th the mass of the Earth or 600 quintillion kg. As for size, it really depends on the composition of the body. The numbers are generally accepted to have a diameter of about 600km for a rocky body.

A quintillion is 1 x 10 to the 18th and Phobos has a mass of 1.0659 x 10 to the 16th kilograms and a diameter of 22 kilometers.