Last Friday the planes were at Los Angeles' Hawthorne airport within approximately 3,600 ft (1,100 m) of each other. There was no risk of a crash, the FAA has said.
Ford, 77, acknowledged and apologized for his mistake, said his representative.
In a statement the representative said the Indiana Jones and Star Wars movie star had a "misheard" instruction from air traffic control.
"The purpose of the flight was to keep the aircraft currency and skill. No one was injured and there was never any risk of collision," the statement said.
Ford was in the controls of an Aviat Husky light two-seat plane.
It is not the first time that Ford, a well-known fan of aviation, has been involved in air accidents.
He flew low in 2017 over an American Airlines aircraft with 110 passengers and crew aboard at John Wayne airport in California. No-one was injured and the FAA decided that no action should be taken.
The actor was injured in 2015, when he crashed his vintage plane on a Los Angeles golf course.
When he was in his 50s, Ford took up flying, and is also trained to fly helicopters.
In 1999, during a training flight in Los Angeles, he crashed his helicopter, but both he and the instructor were unhurt.
A year later a plane had to make an emergency landing in Nebraska which he was flying. His passenger and he again escaped unhurt.