How does this work with Medicaid?

I'd get an opinion from an expert like an Attorney, to see what your options, if any are. It's a huge deal. The amount of the inheritance would make a difference. There are ways to renounce an inheritance. I'd inquire about that as well to see what option is best for your situation.

Your Medicaid, is it through the Affordable Care Act's Medicaid expansion?
if so, it is income based. The $ your received will be considered income the month that you got it and will add into whatever other income you have
(like through a job) and your premium will be based on the income. You'd contact your state's ACA program or exchange to see how it changes your premium (& any copays) and for how long.

But if this is Medicaid though another program, like WIC or disability, it's more complicated. You'd need to speak with your caseworker.

Whichever you don't want to delay as once it's discovered, payments to doctors or clinics could be retroactively clawed back and then you get bills.
It gets really confusing once this starts happening.

If you had to fill out a W-9 and submit to an executor, the estate is going to file a form with the names & SS on all beneficiaries the $ was distributed to. It will go to the IRS and it's a part of estate taxes paperwork. More than likely you won't have to pay any taxes on it. But 6 states do have an inheritance tax (Indiana, Iowa, KY, MD,NE,NJ, PA, TN)