The UKIP leader tweeted he was "at a standstill for 90 minutes" while heading to Thursday's show in Bradford.
Highways England said the the A1 northbound was closed in Nottinghamshire after a fatal crash.
In 2014, Mr Farage missed a UKIP conference after getting stuck in traffic on the M4, which he blamed on high levels of immigration.
A UKIP spokesman said on Thursday Mr Farage was being driven from his home in Kent to the show, which usually starts filming at about 20:30.
He tweeted at 19:35 GMT: "Now been at a standstill for 90 mins on the A1. #bbcqt doubtful. Damn."
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He was replaced on the show by his deputy leader Paul Nuttall, who travelled from Liverpool to face off against Energy Secretary Amber Rudd, Labour's Shabana Mahmood, Lib Dem president Baroness Brinton and political journalist Isabel Oakeshott.
It was the first major televised debate following the announcement of David Cameron's draft EU reform proposals.
Question Time producers tweeted: "We were making plans for @Nigel_Farage - but travel problems mean he'll be replaced by @paulnuttallukip. #bbcqt."
Despite the late line-up change, the show was broadcast at 22:45, starting with a question on Mr Cameron's EU reforms.
Mr Farage blamed his failure to turn up to a reception with supporters in Wales in 2014 on "open-door immigration".
"It took me six hours and 15 minutes to get here - it should have taken three-and-a-half to four," he said at the time.
On the day of the 2010 general election Mr Farage was involved in a plane crash that left him with broken ribs.
Thursday's delays came when the A1 was closed northbound at Coddington following the crash at about 17:30, in which one man was killed.
Nigel Farage missed an appearance on BBC Question Time after getting caught in a traffic jam on the A1.