Does Medicare cover a minimum amount of days for in-patient rehab?

No, there is no set minimum amount of rehab covered by Medicare. What is covered is whatever a doctor certifies is medically necessary. As another comment explains, the dollar cost of the coverage varies for the first 20 days vs. subsequent days up to 100. After 100 there is no coverage whether medically necessary are not. But there is no guarantee of even a day unless a doctor says so

Yes, Medicare will pay in full up to 20 days of rehab afer a minimum of 3 days in the hospital. If the patient continues to show progress, medicare will pay 80% of an additional 80 days. Often, secondary insurance will pay the balance. The Medicare website has a wealth of information --- medicare dot gov