Captive Primate Safety Act - Amends the Lacey Act Amendments of 1981 to add nonhuman primates to the definition of "prohibited wildlife species" for purposes of the prohibition against the sale or purchase of such species in interstate or foreign commerce.

Makes it unlawful for a person to import, export, transport, sell, receive, acquire, or purchase a live animal of any prohibited wildlife species in interstate or foreign commerce (i.e., for pet trade purposes). Modifies exceptions to such prohibition, including by making it inapplicable to a person who is: (1) a licensed and inspected person who does not allow direct contact between the public and prohibited wildlife species, and (2) transporting a single primate of the genus Cebus that was obtained from and trained by a charitable organization to assist a permanently disabled individual with a severe mobility impairment.

Sets forth civil and criminal penalties for violations of the requirements of this Act.