Your social security number (SSN) is required to purchase health insurance through federal and state marketplaces. Your SSN is mainly needed to verify your income with the IRS and help determine if you’re qualified for receiving financial assistance through premium tax credit subsidies.
Additionally, after you choose a plan, the insurance company you sign up with is required to provide a form to you and the IRS which states that you and whoever else is on your plan had minimum essential coverage. This form, known as Form 1095-B will then be used to prepare your individual tax return.
This is especially important if you live in a state that enforces a penalty on state taxes for not having qualifying health coverage!