Anderson, acquired from the Tigers last Thursday, has been with his wife for the expected arrival of a baby boy.
Manager Trey Hillman, called to his Texas home after Sunday's game because of an unspecified emergency, might return for Tuesday night's game against the Seattle Mariners in Kansas City, according to bench coach John Gibbons.
Gibbons managed the club in Monday's game against the Rays.
Mark Teahen, who did not start Sunday's game because of a stiff back, returned to the lineup on Monday. He played third base, giving Alex Gordon a break. Gordon was 0-for-34 in nine games at Tropicana Field.
Teahen, who left Saturday's game in the fifth inning, was a pinch-hitter on Sunday.
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.