The race at Las Vegas Motor Speedway is the third race of the season in NASCAR's Sprint Cup Series. Vickers, 31, will miss the season opening Daytona 500 on Feb. 22 and the next race, at Atlanta Motor Speedway, on March 1.
"The doctors gave me a clean bill of health and said I will be better than before," Vickers said in a statement.
Vickers initially had an artificial patch inserted to fix a hole in his heart in 2010 that also involved blood-clotting problems. It was discovered last month that his body was rejecting the patch so he had surgery to repair the hole.
"The advancements in modern medicine and surgical procedures are amazing," Vickers said.
His team's co-owner, 51-year-old Michael Waltrip, will drive Vickers' No. 55 Toyota in the Daytona 500, a race Waltrip won in 2001 and 2003. A substitute for Vickers at Atlanta has yet to be named.
NASCAR, meanwhile, said that after reviewing "the circumstances surrounding the situation," Vickers remains eligible to qualify for NASCAR's Chase for the Cup title playoff despite missing the season's first two races.
Vickers has won three races and 12 pole positions in 316 starts in the Cup series, the most recent victory coming at New Hampshire in July 2013.
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