The backup point guard suffered the injury Sunday against the Brooklyn Nets, the first game of a four-game road trip. He was sent home to undergo further testing.
An MRI on Tuesday revealed a bone bruise and a Grade 3 sprain, sources say.
Dellavedova has appeared in 37 games and is averaging 4.4 points and 3.8 assists while shooting 38 percent from beyond the arc.
The Bucks are 29-23, sitting fifth in the Eastern Conference standings. They have won seven of their past 10 games.
Last week the Bucks lost second-year guard Malcolm Brogdon for six to eight weeks with a torn tendon in his left quad.