Gibb had been in a critical condition in hospital after suffering a heart attack during an operation to remove an intestinal blockage after he collapsed at his Florida home last week.
His wife, Yvonne, and his two children had been with him at the Mount Sinai Medical Centre in Miami since the surgery on Thursday night.
A statement released by his family said: “It is with great sadness and sorrow that we regretfully announce the passing of Maurice Gibb this morning.
“His love and enthusiasm and energy for life remain an inspiration to all of us. We will all deeply miss him.”
His family and fans outside the hospital had been hopeful he was showing signs of recovery as he opened his eyes for a brief time and squeezed his daughter’s hand.
The family statement said that he died at 1am.
As a member of the Bee Gees, Maurice Gibb had been one of the best-known faces in show business for the last four decades. He, his twin, Robin, and elder brother, Barry, started their singing careers in the 1950s, earning their name from a previous incarnation as the Brothers Gibb.
Following a spell in Australia, where they gained their first recording contract, they returned to Britain in 1967 to critical acclaim. Their distinctive, close-harmony singing became their trademark and survived musical fashion and family rifts.
Their hits include the soundtrack to the film of the disco phenomenon, Saturday Night Fever in 1977 and a sequel, Stayin’ Alive in 1983.
Saturday Night Fever saw some of the group’s most successful tracks such as Stayin’ Alive, How Deep Is Your Love and Night Fever. One of their most successful collaborations was with Motown legend Diana Ross on Chain Reaction in January 1986.
In 1987, after several years of writing and producing acts as diverse as Barbra Streisand to Dolly Parton, they were again at the top of the charts with You Win Again. Their last album together was in 2001, entitled This Is Where I Came In.
Maurice, bass guitarist and keyboard player in the group, had well-documented problems with alcohol. He met his first wife, the singer Lulu, in the BBC canteen. They married in 1969 but divorced four years later.
Pete Bassett, Robin Gibb’s spokesman, said: “It’s a huge shock to us all and completely unexpected. Robin and his family have flown out to Miami and everyone is just devastated. They have literally woken up to this and it’s the worst possible news anyone could have expected from the day’s events. There’s just complete and utter shock. This is an unbelievable blow.”
“Maurice was part of one of the most influential music families in music history so his death will be a huge loss.”
Music industry commentator and DJ Paul Gambaccini said: “Maurice was a talented multi-instrumentalist, playing keyboards, guitar, bass and percussion.
“On the vocal side, he was the high part of the three-part harmony... therefore, you can’t take him away from the other two. I’m afraid that this beautiful Bee Gee sound without him can never be produced again.
“Maurice himself said: ‘One of us is OK, two of us is pretty good, but three of us together is magic’.”