Leopold suffered the injury to his hand in a Nov. 7 game against the Flames.
"He's going to be operated on this week and we'll reevaluate him in two months and see how he goes," Blues coach Ken Hitchcock said on Monday (via Lou Korac). "In eight weeks we'll take a reevaluation of the hand and go from there.
"He has a ligament issue, need to get it solved right now so that he's back playing during the season. We'll get him looked at here and have that operation done as quickly as possible and then he'll get back playing in hopefully two months."
In Leopold's place on defense the Blues are going to turn to Ian Cole, who was recalled from AHL Chicago.
Leopold has two assists in 13 games this season for the Blues, averaging 15:45 per game. He played in 15 games for the Blues last season after a deadline trade to St. Louis from Buffalo.