He will be reevaluated in four weeks, and the team said it is hopeful for his return sometime in March.
Curry sustained the injury during an Oct. 30 loss to the Phoenix Suns and had surgery on the hand on Nov. 1 in Los Angeles and then a second procedure in early December to take pins out of the hand as he continued his rehab process.
"He's made some big strides," Warriors coach Steve Kerr said before Saturday's game against Cleveland. "I guess the word is a month away from having another evaluation. We're really hopeful that around that time he'll be able to play. We'll determine that around March 1."
Over the past few weeks, Curry has started to become more visible during Warriors games and practices. The star point guard has been working with Warriors staff members after practices to get more shots up and shake the rust off from his injury.
"He needs to progress over the next month to lot of action -- one-on-one, 3-on-3, 5-on-5," Kerr said. "That's all part of the plan."
Kerr said recently that he has asked Curry and Klay Thompson, who continues to rehab a torn left ACL sustained in last year's NBA Finals, to be around the team more and offer guidance to the group's younger players. It remains unclear whether Thompson will play again this season, but an update on his status is expected after the All-Star break.
Golden State (10-39) has the NBA's worst record without Curry, the two-time MVP who led the Warriors to three titles and five straight Finals appearances. Curry is averaging 23.5 points in 11 seasons.
"It's good to see Steph on the floor and on the sidelines with the team and traveling," Kerr said. "The mood is brighter when Steph is around. He's giving the young guys a lot of words of wisdom."
ESPN's Nick Friedell and The Associated Press contributed to this report.