William Bennett, 56, the principal oboist, was performing Richard Strauss' Oboe Concerto during an 8 p.m. performance at the hall, located at 201 Van Ness Ave., when he fell to the stage, spokesman Oliver Theil said.
The show was stopped and he was taken to a hospital, where it was determined that he had suffered a brain hemorrhage, Theil said.
He was still at the hospital Monday morning and was listed in guarded condition, according to Theil.
"We all think the world of Bill, and our thoughts and best wishes are with him and his family," Theil said.
Bennett has been a member of the symphony since 1979 and has been the principal oboist since 1987.
There has been an outpouring of support for Bennett over social media, including by the New York Philharmonic, which sent well wishes in a tweet Monday morning.