Kristen Foster, a publicist for the guitarist, said Tuesday that Clapton was doing well and recuperating with his family in England.
The hall says Jeff Beck will replace the 64-year-old guitarist for Friday night's show at Madison Square Garden.
Clapton was to perform as part of a two-night celebration in honor of the hall's 25th anniversary. Beck now joins U2, Aretha Franklin and Metallica for the final night.
The Thursday lineup includes Crosby, Stills and Nash; Stevie Wonder; and Bruce Springsteen and the E Street Band. HBO will air the concerts Nov. 29.
Clapton's Web site says he remains committed to his 2010 concert schedule.