Kind of, your question its kinda open because each gem has different properties and form in different ways, there are only three ways of this to happen:
1.- Your planet has an huge pressure within its surface or its a gas giant, it's thought that in some of this places the pressure its so high that diamonds form in the clouds and come raining to lower parts of such atmosphere.
2.- Meteoric origin, given an extraordinary set of coincidences, meteors which had huge mineral deposits impacted on the planet itself in a geologically small amount of time relatively close in time to the present
3.- Mixture of both, in some random event a gas giant loses it's gas leaving behind only its rocky core which could be made entirely of such minerals,
The second one its more complicated as density would make such minerals sink in just a few million years into the soil, that's actually why the Earth surface its so poor in minerals and why we have to dig for them.
Other than that... I don't see any good way of this happening, not in our universe at least