In March this year, the broadcaster decided to halt production following the December 2022 accident which occurred during filming.
On Tuesday it said: "Given the exceptional circumstances, the BBC has decided to rest the UK show for the foreseeable future... We know resting the show will be disappointing news for fans, but it is the right thing to do."
"All other Top Gear activity remains unaffected by this hiatus including international formats, digital, magazines and licensing," the BBC statement said.
Flintoff, 45, a former England cricketer who became a Top Gear host in 2019, was said to have been lucky to survive the accident at Top Gear's test track in southern England.
Recent photos show a facial injury.
The Sun newspaper reported last month that his injuries were "life-alteringly significant", citing his legal team.
He reached a settlement over the accident worth £9 million ($NZ18.6 million) with the BBC's commercial arm, BBC Studios, the Sun report said.
Last week, Flintoff was named head coach of an English cricket franchise and in September joined the England team in an unofficial coaching role.
A safety review of the show was carried out in the months following the crash which the BBC said showed that while best practice was followed, there were important learnings which would be "rigorously applied" to the programme in future.
The broadcaster, which has apologised to Flintoff, said it remained committed to the former cricketer and his two co-presenters, and there were new projects being developed with them.