The woman said she was in her car running errands when a man in a car followed her to the mosque's parking lot on the west side of Columbus on Monday afternoon.
The woman told reporters the man harassed her, swore at her, said she should leave the country and threatened to kill her. He then attacked her with pepper spray, she said.
Mosque officials called police, who took a report and turned it over to the prosecutor's office.
The FBI said Tuesday it will likely open a civil rights investigation, the results of which would be turned over to federal prosecutors for any possible charges.
A mosque security camera recorded the encounter. The video, which was shown to reporters, shows the woman pulling into the parking lot, another vehicle pulling in and blocking hers, and then a man getting out and angrily talking to her. The alleged pepper-spraying was not visible, because the woman's car blocked the camera's view.
Abdiaziz Abdi, a spokesman for the mosque, said the camera was installed about a year ago because several cars had been vandalized.