Robin Gibb composed the symphonic piece with his son, Robin-John Gibb, and was scheduled to perform a new song, "Don't Cry Alone," during the premier concert at The Royal Albert Hall.
But in a message read out to the audience, Robin-John said his 62-year-old father is still in hospital.
"He sends all his love," he said ahead of the performance. "We are all praying for him and hoping he has a speedy recovery."
Robin Gibb's publicist Doug Wright said he is in stable condition in the hospital. He did not provide more details.
Gibb had intestinal surgery last month, and was hospitalized late last year for stomach and colon problems. He has not disclosed the nature of his illness, but has said a growth on his colon has been removed.
The requiem, performed by the Royal Philharmonic Orchestra, commemorates the April 1912 sinking of the ocean liner and the loss of more than 1,500 lives.
The Bee Gees had a string of hits in the disco era including "Stayin' Alive."