The Heat said the hope is that the procedure and some rest will allow the knee inflammation to subside by next week.
Dragic is averaging 16.3 points, 4.7 assists and 3.3 rebounds in 30.8 minutes per game.
He missed two games early this month, then came back for four games before the swelling returned. He was held out of Sunday night's game against the Los Angeles Lakers.
"There are no absolutes in this league and every case is different," Heat coach Erik Spoelstra said Sunday. "His knee hasn't responded the way any of us had hoped when you're playing games constantly."
The Heat (6-10) host Brooklyn on Tuesday, then travel to Chicago on Friday and Toronto next Sunday.