The team said Rush was scheduled to have an MRI on Saturday. The results of an X-ray were not announced.
Rush leaped in the air for a dunk when Zach Randolph fouled him from behind with 4:09 left in the first quarter. Rush landed awkwardly, his knee bent badly and he tumbled to the court.
He got up on one leg, waved his arms violently in the air and shook off teammates who tried to help. Rush covered his face in agony and eventually limped to the locker room with the support of teammate Jeremy Tyler and trainers.
Memphis selected third-string center Andris Biedrins to shoot the free throws. The home fans booed Biedrins -- the former starter -- when he checked in just as they did during team introductions earlier on opening night. Biedrins, owed $9 million this season with a $9 million player option for 2013-14, missed both free throws.
The 27-year-old Rush appeared in 65 of 66 games last season after coming over in a trade from Indiana for Lou Amundson. He posted career highs by shooting 50 percent from the field and 79 percent on free throws, fitting seamlessly into coach Mark Jackson's system and staying steady despite a rash of injuries that shattered the roster.
Rush averaged 9.8 points and 3.9 rebounds in 26 minutes per game last season. He shot 45.2 percent from 3-point range -- sixth-best in the NBA -- and was Golden State's best option off the bench.
Rush was originally drafted 13th overall by Portland in 2008 after leading Kansas to the national championship. He was then traded to Indiana along with Jarrett Jack and Josh McRoberts for Jerryd Bayless and Ike Diogu.