Hendriks was slated to be released after spending Saturday in a Baltimore-area hospital.
Twins manager Ron Gardenhire said doctors at the hospital recommended the pitcher stay another night, leaving open the possibility that Hendriks would not accompany the team from Baltimore to Minnesota after Sunday's game.
Gardenhire said, "I don't think it would be a good idea for him to get on an airplane."
Hendriks missed his scheduled start Sunday. He was replaced by long reliever Anthony Swarzak.
It was uncertain if Hendriks would miss another turn in the rotation.
Gardenhire said, "He hasn't touched a baseball for a few days now, plus he's been pretty sick."