Scott Hutchison, 36, has not been seen since leaving the Dakota Hotel in South Queensferry at 1am on Wednesday.
His brother and bandmate Grant Hutchison described him as being in a “fragile state”.
He added: “We’re all incredibly worried. He was in the hotel in South Queensferry and hasn’t been seen or heard from since 1am.
“His phone is with the police. If somehow you are reading this Scott then can you just let someone know you’re safe please? We love you very much x.”
The band said on Twitter on Thursday morning there had been no news and thanked fans for their “support and kindness”
Messages of hope were sent from friends, family and fellow musicians, including Gary Lightbody from Snow Patrol.
There was also support from authors Irvine Welsh and Christopher Brookmyre, and radio presenter Edith Bowman.
Hutchison is described as white, 6ft tall with a stocky build, dark hair and a thick beard.
He was last seen wearing a dark baseball cap, navy blue hooded jacket, grey or khaki trousers and white trainers.
Police Scotland said there was no update on the search for the singer, who lives in Dennistoun, Glasgow.
Anyone with information should contact officers at Drylaw Police Station via the 101 number.