The slugger was sent to Minneapolis from Arlington, Texas, Thursday when the infection did not improve. Rangers doctors gave him medication this week, but it proved ineffective.
The Twins said Friday that Morneau will spend the next three days recovering at home.
"We'll see where he's at Monday," Manager Ron Gardenhire said on the team's Web site. "That's all we can do. (Doctors) think by the weekend it should be cleared if he relaxes a little bit."
But if the infection persists and Mourneau continues to suffer dizzy spells, he'll be put on the 15-day disabled list, Gardenhire said.
Mornueau is batting .298 with 28 homers and 94 RBI.