What is the treatment for avulsion fracture of the thumb?

It depends: It really matters where the frature is, how large it is and whether or not it involves the articular margin. It can be treated by a splint, cast or even surgery. The specifics would come from a hand surgeon who could tell you the correct treatment. Go see a specialist.

Dr Ali and another doctor agreed

In an adult an : Avulsion involves the collaeral ligament of the mp joint, then typically surgery is considered unless one can prove the joint is stable or will be if the fracture heals. For the tip of the thumb a volar plate injury may be observed but one needs to be wary of a flexor tendon avulsion. For the base of the thumb it depends upon the size and detraction of the fragment. Much depends where it is!