The Red Wings recalled defenseman Xavier Ouellet from AHL affiliate Grand Rapids to replace Smith, who will be out a minimum of seven days.
Smith came down with the infection as a result of his fight with Columbus Blue Jackets winger Nick Foligno in the third period of Detroit's 5-0 win over Columbus on Tuesday night. Smith had two assists in the win.
According to MLive.com, Smith can't currently put on his glove and is on medication to help prevent further infection.
Smith, a fourth-year pro, has six points in 18 games this season and is averaging a career-high 19:35 of ice time this season.
The Red Wings have 23 points this season and are in fourth place in the Metropolitan Division. They travel to the Winnipeg Jets on Thursday.
- Ben Estes