Westbrook went under the knife to repair a ligament in his left hand and had also undergone an arthroscopic procedure on his right knee, the club said.
The 2016-2017 NBA MVP is expected to be fit to return to basketball activities in three weeks, the club said.
George meanwhile had elective surgery on his right shoulder to address a tendon tear. He also faces further surgery on his left shoulder to repair a torn labrum, the team said.
No timetable was given for George's likely return, with the club saying only that an update would be given ahead of the 2019-2020 season.
Westbrook and George were key figures once again for the Thunder this season before the team exited in the opening round of the playoffs.
Westbrook averaged a triple-double for the third consecutive year (22.9 points, 11.1 rebounds, 10.7 assists), the first player in NBA history to accomplish the feat.
George meanwhile averaged career highs in points (28), rebounds (8.2), assists (4.1) and steals (2.21).