This little egg seems to be curled up against a hat. You probably shouldn't move that. Perhaps another person or member of the family put it there to keep the young inside warm.
The Mico is known to live in groups consisting of two to fourteen members. Without some family nearby, these creatures become rather distant and anti-social. The main diet for these creatures is sap from various trees found around Ark. So if your little Mico is gone for a few hours, don't fret. They probably just went out in search of food. The Mico rarely spend time on the ground and prefer to be up high in trees. So hopefully your home has lots of places for your little creature to play! The hat they are presented with before birth is always kept with them. It is almost like a family heirloom, although is never passed between Micos.