The clot was found after a Monday examination and he was placed on blood-thinning medication that will prevent him from racing. Vickers missed the final 25 races of the 2010 season with blood clots, and during that time required heart surgery.
He said in a statement his physicians are confident he'll be able to resume activity before the 2014 season.
"If there's anything to be positive about with today's news it's that this is only a temporary setback," Vickers said. "The timing for this is never good, but I'm glad we'll get it out of the way now and be ready to run for a championship with the Aaron's Dream Machine in 2014."
Michael Waltrip Racing named Vickers the full-time driver of the No. 55 Toyota in August. He'd previously shared the seat with Mark Martin and team co-owner Michael Waltrip.
Waltrip had already planned to drive the car this weekend at Talladega, and the team said it will decide later on its driver for the remaining four Sprint Cup Series races.
"We were just informed this morning and our concern is for Brian's health," MWR co-owner Rob Kauffman said. "Anything else will be worked out in due course."
Joe Gibbs Racing did not name an immediate replacement for Vickers in the Nationwide Series, which is off until Nov. 2 at Texas.
"We are praying Brian will have a quick and full recovery from this latest issue," team owner Joe Gibbs said in a statement. "Everyone at JGR appreciates all the hard work and effort he has given to our Nationwide Series program this year. He is a great competitor and we look forward to seeing him back on the track in 2014."
Vickers was scheduled to participate in a Sprint Cup Series test Monday at Charlotte Motor Speedway, but MWR instead used Brett Moffitt.
Vickers has run 22 races with MWR. He has 10 top-10 finishes and won at New Hampshire in July, a victory that solidified his full-time hiring in the No. 55. The win ended a 75-race winless streak for Vickers.
His hiring by MWR was to mark a return to a full Cup ride for Vickers, who last ran for the championship at NASCAR's top level in 2011. He lost that seat when Red Bull Racing pulled out of NASCAR and Vickers ran just eight Cup races in 2012 for MWR.
He was hired by JGR this year to run for the Nationwide title, 10 years after he won the series championship driving for Hendrick Motorsports. But Vickers is winless in Nationwide this season and eighth in the standings.
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