Medicare Patient Empowerment Act of 2021 This bill allows any Medicare beneficiary to enter into a contract with an eligible professional, regardless of whether the professional is a participating or non-participating physician or practitioner, for any item or service covered by Medicare. Such beneficiaries may submit a claim for Medicare payment in the amount that would otherwise apply, except that, where the professional is considered to be non-participating, payment shall be paid as if the professional were participating. An eligible professional is a physician, physician assistant, nurse practitioner, clinical nurse specialist, certified registered nurse anesthetist, certified nurse-midwife, clinical social worker, clinical psychologist, registered dietitian or nutrition professional, physical or occupational therapist, qualified speech-language pathologist, or qualified audiologist. A Medicare beneficiary must agree in writing in such a contract to (1) pay the eligible professional for a Medicare-covered item or service; and (2) submit, in lieu of the eligible professional, a claim for Medicare payment. However, a beneficiary may negotiate, as a term of the contract, for the eligible professional to file such claims on the beneficiary's behalf. The bill preempts state laws from limiting the amount of charges for physician and practitioner services for which Medicare payment is made.