There does not seem to be any formal age requirement.
This is sort of confirmed by 37 CFR § 1.63(c) (which relates to the requirement to provide an inventor's oath), which provides (emphasis added):
A person may not execute an oath or declaration for an application unless that person has reviewed and understands the contents of the application, including the claims, and is aware of the duty to disclose to the Office all information known to the person to be material to patentability as defined in § 1.56. There is no minimum age for a person to be qualified to execute an oath or declaration, but the person must be competent to execute, i.e., understand, the document that the person is executing.
Anectodally also, the USPTO Kids site seems to have stories of minors applying for patents.