The All-Star suffered the non-displaced fracture in the fifth metacarpal in the first quarter of the Cavs' 125-114 loss to the Detroit Pistons on Tuesday. Instead of surgery, Love will undergo rehabilitation to repair the injury.
Love visited Dr. Michelle Carlson at the Hospital for Special Surgery in New York on Thursday. He was accompanied by the Cavs' medical team, including team physician Dr. James Rosneck, and Dr. Steven Maschke of Cleveland Clinic Sports Health.
Love is Cleveland's leading rebounder (9.4 per game) and second-leading scorer (17.9 points per game).
The Cavaliers won their first game without Love, beating Miami on Wednesday. They next will host the Houston Rockets on Saturday.
Love underwent surgery on the same hand in October 2009. That procedure required three screws to be inserted.
He was selected as a reserve for this year's All-Star Game but was replaced by Miami's Goran Dragic on Thursday. The All-Star Game will be played Feb. 18 in Los Angeles.
ESPN's Dave McMenamin contributed to this report.