Vickers, 31, 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 week that his body was rejecting the patch, so on Saturday, "I had to have corrective surgery to repair the hole and now I am beginning the recovery process," the driver said in a statement.
"I have faced obstacles before and it has made victory that much sweeter and I know that will be the case again," Vickers said. No timetable was given for his return.
Vickers has won three races and 12 pole positions in 316 starts in NASCAR's Sprint Cup Series, the most recent victory coming at New Hampshire in July 2013.
Vickers joined MWR in 2012, and he finished 22nd in the championship standings this year with three top-five finishes in 36 races.
He had been driving the team's No. 55 Toyota, and MWR said it had not made a decision on a replacement driver for the start of the 2015 season.
"As this is fresh news, we will adjust our future plans as more information becomes available," team co-owner Rob Kauffman said in a statement.
The NASCAR Sprint Cup season opens with the Daytona 500 on Feb. 22.