Annuities are very complicated and often sold to individuals without considering their interplay with Medicaid eligibility. While there are various forms of annuity contracts, an annuity is either qualified or non-qualified.
A qualified annuity is like an individual retirement account in that Medicaid will not take the principal balance of the annuity so long as you are receiving your required minimum distributions.
A non-qualified annuity is not protected. Owning a non-qualified annuity is no different than having cash in a bank account.
If you are unsure as to which type of annuity you have, you should review your last statement. In most cases, if you walked into a bank, you were sold a non-qualified annuity. Qualified annuities are usually purchased with the rollover proceeds from retirement accounts with your employer.