Beady Eye guitarist Gem Archer is set to "make a full recovery over the next few weeks", according to the band.
A statement on their website says they are still planning to perform together later in the year.
The 46-year-old was taken to hospital this month after having an accident which caused a "severe head trauma".
Beady Eye, which also features former Oasis frontman Liam Gallagher, had to pull out of a number of gigs, including a set at V Festival over the weekend.
The statement thanked fans for their support over the past few weeks.
"He and his family really appreciate it and so do the band," it said.
"We are gutted about all the cancelled shows but thank you for understanding that we need to prioritise our mate and his recovery."
The 46-year-old is "doing well so far" and should make a full recovery in the coming weeks. There are no further details on his injury, or what caused the accident.
This is just to say thanks for your patience, and for all the messages that have come in from all over the world," the statement ended.
"We are buzzing about getting back on stage for the UK and Ireland dates in November."
Gem Archer's wife, Lou, has also been tweeting about his recovery.
She said: "He needs to mend, how long it will take I'm not sure. He's a tough cookie."
Along with Gem Archer and Liam Gallagher, Beady Eye features guitarist Andy Bell, who also found fame in Oasis.
Former Kasabian guitarist Jay Mehler joined the group earlier this year.
Beady Eye's second album, BE, was released on 10 June.
They worked with Yeah Yeah Yeahs producer Dave Sitek, who Liam Gallagher described as "without a doubt the best producer I've ever worked with, a real outlaw".
He added: "When we were writing it, we really got our heads down. [We had] clear heads."
The band has featured on a number of festival line-ups this year, including T in the Park and Glastonbury.