"First and foremost our thoughts are with Brian and his family,” MWR co-owner
But in a meeting with reporters Friday at Auto Club Speedway, Waltrip acknowledged that "obviously this is a setback for our team."
The team said Brett Moffitt, 22, would drive Vickers' No. 55 Toyota this weekend in Fontana.
Vickers missed the first two races this season, at Daytona and Atlanta, while recovering from corrective heart surgery last December. The surgery was to repair a patch on a hole in his heart, a patch first inserted in 2010.
Waltrip drove Vickers' car in the Daytona 500 and finished 26th; Moffitt drove the car at Atlanta Motor Speedway and finished eighth.
"We are fortunate to have Brett Moffitt in our system and marveled at his great drive in Atlanta three weeks ago, so we know he can get the job done in the No. 55 this weekend," Waltrip said.
As for other upcoming races, "as this news is very fresh and the situation is very fluid, we can only plan for this weekend at this point," Waltrip said.
Vickers finished 15th at Las Vegas in his return to the Sprint Cup Series on March 8, but was involved in a crash on the first lap at Phoenix last Sunday and finished 41st.
"Thankfully, because I recognized the signs and symptoms, the doctors caught this early and I'm going to be OK," Vickers said in a statement. "I'm going to follow [the] doctors' orders and do everything I need to do to get well."