The accident occurred on Monday, when Flintoff, 45, was filming in icy conditions at Dunsfold Park Aerodrome in Surrey.
“Freddie was injured in an accident at the Top Gear test track this morning – with crew medics attending the scene immediately,” the BBC said in a statement.
“He has been taken to hospital for further treatment and we will confirm more details in due course.”
Flintoff’s injuries are “not life-threatening”, according to The Sun, which added that he had been “driving on the track as normal” and was not going at high speeds.
“All the usual health and safety measures were in place for filming too,” a source told The Sun. “Freddie was taken to hospital by air ambulance shortly afterwards.
“Filming has been postponed for now and all anyone cares about is Freddie recovering.”
Flintoff’s co-star Chris Harris, who presents the show along with Paddy McGuiness, was also present at the test track.
In 2019, Flintoff survived a 125mph crash during the filming of another episode of Top Gear, declaring himself “absolutely fine” as he walked away from the accident.
He said at the time: “I go to great lengths to make sure I do well in Top Gear drag races but, on this occasion, I went a few lengths too far. It will look more ridiculous than dangerous when you see it on TV.”