It said it would “continue to support” Flintoff with his recovery.
“Under the circumstances, we feel it would be inappropriate to resume making series 34 of Top Gear at this time,” the statement added.
“We understand this will be disappointing for fans, but it is the right thing to do, and we’ll make a judgment about how best to continue later this year.
“This has also impacted the production team, who we continue to support.
“Finally there will be a health and safety review of the show, in line with our procedures.”
Flintoff, 45, was taken to hospital after the crash at the show’s famous track at Dunsfold Aerodrome on 13 December.
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The Sun reported he was behind the wheel when the crash happened and was airlifted to hospital, but a source told the paper his injuries were not life threatening.
The Health and Safety Executive (HSE) said at the time that it was “making inquiries”.
In 2006, former Top Gear presenter Richard Hammond was involved in a life-threatening crash during filming.
Flintoff – popularly known as “Freddie” and famous for his England cricket heroics – has hosted the show alongside Chris Harris and Paddy McGuinness since 2019.
He also appeared for many years on Sky panel show A League Of Their Own.
No episodes of Top Gear series 34 have been broadcast, with season 33 airing at the end of last year.