Osgood is expected to return to Detroit on Sunday and then visit a doctor in Philadelphia later in the week.
"It's been a nagging groin injury and we want to get to the bottom of it," Red Wings general manager Ken Holland said Saturday. "Let's get an expert opinion, and if he needs surgery we'll get surgery. If the doctor feels he just needs time, then we'll take their lead."
The Red Wings are expected to call up Joey MacDonald from the American Hockey League as they continue a five-game road trip in Colorado on Monday.
Osgood, who has won three Stanley Cup titles with Detroit, backed up Howard most of the last two seasons. Last month, he became the 10th goalie to win 400 NHL games.
He earned a victory in his last start on Tuesday in Edmonton, but with the pain lingering, Holland said it was important to get answers soon.
"It's the middle of January and the playoffs are three months away, so if we're going to do something, now is the time," Holland said.