The illness could keep the 2007 Daytona 500 winner from competing in Saturday's Budweiser Shootout at Daytona International Speedway.
Saturday's race includes the 12 drivers who competed in the 2009 Chase for the Sprint Cup championship, including four-time points champion Jimmie Johnson.
The statement said Harvick hopes to arrive in Daytona Beach before Saturday's race.
He has received medical attention, and because he won the Shootout in 2007, Harvick is an automatic entrant for the 2010 "500", based upon new NASCAR guidelines.
Childress Racing teammate Clint Bowyer, the driver of RCR's No. 33 Cheerios/Hamburger Helper Chevrolet, did not qualify Thursday for this year's non-points event.