Red Bull Racing general manager Jay Frye says Vickers is on medication and was hopeful of being released from the hospital on Friday.
Frye says Vickers complained of discomfort on his chest and went to the hospital. He says the team is not sure what caused the clots.
Frye says there is "no timetable" for Vickers' return.
The 26-year-old is in his seventh full season racing in NASCAR's elite Sprint Cup Series. He has two career Cup wins and made the 12-driver Chase for the championship last season.
He's currently ranked 20th in the standings.
Casey Mears will replace Vickers in the No. 83 Toyota.