The move — first reported in the Richmond Times-Dispatch — came as a surprise, as the Republican had previously said he would serve out his term and try to help GOP candidates win elections this fall.
Cantor, a major fundraiser with close ties to big business and Wall Street, did not say specify what he plans to do after leaving Congress. He said only that he wants to advocate as a private citizen "for the conservative solutions to the problems we face that will secure our nation's greatness and provide a better life for all Americans."
Cantor said a special election on Nov. 4 — the same day as the scheduled regular election — would give the winner seniority rather than waiting until January to take office with the new Congress. He also noted that special election on the same day as the scheduled general election would not cost taxpayers extra.
McAuliffe spokesman Brian Coy said Friday morning that the governor's office was reviewing the request for a special election.
Cantor lost to Dave Brat, an underfunded, tea party-backed opponent, in the June Republican primary. The 7th District is heavily Republican and Brat is considered the early favorite against Democrat Jack Trammell.
"It is vitally important that the constituents have a clear and strong voice during the consequential lame duck session of Congress," Cantor said. "I believe and hope that voice will be Dave Brat."
Brat, who was highly critical of Cantor during the primary campaign, thanked his former opponent for his endorsement.
"The time one has to sacrifice to be an elected official is enormous, and he has sacrificed a great deal to serve the people," Brat said in a statement Friday.
Cantor, 51, is a seven-term House veteran who before his defeat had been seen as a potential rival — and likely successor — to House Speaker John Boehner, R-Ohio. Cantor appointed to his first leadership position in 2002, when he was named chief deputy whip of the party and became the highest-ranking Jewish Republican in Washington.
Though he had a conservative voting record, he was distrusted by some tea party supporters who suspected he might be too eager to reach compromise on immigration legislation.