Some may require it. But, if your credit history is good you can always look for a lender that's more flexible. Don't forget to check out any credit unions that are available to you. Often their rates are cheaper than banks. There are two other popular methods of financing cars to consider.
Some homeowners choose to borrow against the equity in their house and use that money to buy a car.
And, generally, a home equity loan carries a lower APR than a car loan. But, it's important to repay the loan in a timely manner. Another option is to tap into your 401k retirement plan. Many 401k plans will allow you to borrow to buy a car. This can be a good idea, but you do need to be careful.