Indians manager Manny Acta said Hannahan is day to day with tightness in his lower back.
Acta also said Hannahan may start on Tuesday, but that he felt the tightness on Sunday in the Indians' 12-1 loss to the Red Sox.
Jose Lopez started at third base and batted seventh on Monday.
Hannahan started at third base and later moved to short on Sunday in the series finale in Boston. He played the entire game, going 0-for-3 with a run scored.