It takes approximately 6-8 weeks with a cast. If you do not have a cast it will take a lot longer because if you do not have it in the straight position in the healing process it could form the wrong way and you will be scarred for life.
If the broken pieces of the metacarpal are lined up well, it takes six weeks for new, strong bone to form around the fracture site. This is generally true whether or not you have surgery. Healing...