Probably once a month I get asked, “Is there a minimum personal injury settlement amount?” And the answer is no. Theoretically.
Theoretically, a person could settle their case for one dollar or fifty cents. In the real world, perhaps the question is, “If I have a very very small injury–let’s say I hurt my neck–I got checked out in the emergency room, took some Aspirin for three days and I’m fine, and the only bill I had to pay was a fifty dollar deductible to my health insurance. Am I going to be able to find a lawyer?” Typically I would say no. You probably won’t be able to find a lawyer. Because–at least speaking for myself–it kind of doesn’t make any sense for either you the client, or for me. So there’s no minimum amount.
On the other hand, if the accident is that minor, and the other person’s at fault, there’s no reason for you not to call up the other person’s insurance company and just negotiate a small settlement on your own.