The 25-year-old right-hander left his start Thursday night with elbow pain that he said had been bothering him for a while.
Whitley is 5-5 with a 5.02 ERA in his two years in the majors. Last year, Whitley started off his career in style, going 3-0 with a 2.56 ERA in his first seven starts, but is just 1-2 with a 4.19 ERA this season.
Tanaka, on the DL with a mild right forearm strain and tendinitis, made some progress Monday by throwing 29 pain-free pitches during a bullpen session at Nationals Park.
The team is expected to announce a minor league rehab start for Tanaka later in the week, and he could rejoin the major league team by the end of the month.
While Tanaka was able to avoid Tommy John surgery last season after a small tear in the ulnar collateral ligament of his right elbow was found, Nova was not so lucky.
The Yankees are hoping that Nova can return next month after being out since undergoing surgery last April to repair his UCL.