Morneau has not played since April 16 because of a nasty bout of the flu, which has circulated through the team in the past 10 days. He would have missed six games in a row, but the series opener against Cleveland on Friday night was postponed by rain.
The illness made his return from missing the last three months of the 2010 season with a concussion even more difficult.
Morneau is hitting just .208 with no homers and three RBIs in 14 games.
Delmon Young also has been fighting the flu, as well as a rib injury.
Young was scratched for the fourth straight game Saturday, but manager Ron Gardenhire says he hopes to have Young back Sunday in the series finale.