The cricketer-turned-presenter was airlifted to hospital last December after crashing while filming a car review at Dunsfold Park Aerodrome, home of the Top Gear test track.
In a statement, the BBC said: “Under the circumstances, we feel it would be inappropriate to resume making series 34.
“We have sincerely apologised to Freddie and will continue to support him with his recovery.
“We understand this [halting the show] will be disappointing for fans, but it is the right thing to do, and we’ll make a judgement about how best to continue later this year.”
The broadcaster added that it would be conducting a health and safety review of the show.
Earlier this year, it was reported that Flintoff was putting his TV career “on hold” at the behest of his family in order to focus on his recovery.
While insiders said at the time that his injuries were non-life threatening, his 16-year-old son Corey said that the 45-year-old was “lucky to be alive”.
“It was a pretty nasty crash. It is shocking. We are all shocked but just hope he’s going to be OK,” he said.
Flintoff has presented Top Gear since 2019 alongside Paddy McGuinness and Chris Harris.
He narrowly avoided serious injury in an earlier crash not long after joining the show, explaining he “ran out of runway” at Elvington Airfield near York while riding a specialised three-wheel drag racing vehicle in competition with his fellow presenters.
In a statement at the time, Flintoff said: “I’m absolutely fine and was back filming today. 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!”
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The airfield is the same one where former Top Gear presenter Richard Hammond crashed in 2006 while piloting a drag racing car.
Hammond spent two weeks in a coma after crashing at 288mph and suffered paranoia, memory loss and depression as a result of brain damage caused by the crash.
Flintoff retired from professional cricket in 2009, spending several years as a team captain on the Sky sports panel show A League of Their Own, hosted by James Corden.