There's no universal minimum to finance a car — approvals happen across the whole credit spectrum — but your rate falls sharply as your score rises. Prime borrowers (661+) get materially lower APRs than subprime borrowers (501–600), a gap that can total thousands of dollars over a typical loan.
Auto lenders approve borrowers across the credit spectrum, so a low score rarely means an automatic 'no.' What changes most is the interest rate. Lenders group applicants into credit tiers, and APRs rise steeply as you move down them.