Laney had an arthroscopic partial meniscectomy on her right knee, the team announced.
Laney, who was the Liberty's leading scorer last season at 16.8 PPG, played four games this season for New York - the last of which was May 17 -- and averaged 13.3 PPG.
Laney had arthroscopic surgery on her left knee last November; she had originally torn her left ACL during the 2016 season. She was the WNBA's most improved player in 2020 while with Atlanta, and then signed as a free agent with the Liberty for 2021.
If Laney is able to return after eight weeks, the Liberty have seven games in August, with the regular-season finale Aug. 14.