A cyclist shot an arrow at a man sleeping by a Brisbane bikeway in what police believe was an attempted murder.

The 51-year-old victim was asleep near the Queen Street pylon in the city when another man rode past him shortly after 10pm (AEST) on Sunday, police say.

The offender rode back a few minutes later and fired a single arrow into the man's body before riding off along the Bicentennial bikeway, carrying a large duffle bag.

The victim walked to a nearby convenience store and called police.

He underwent emergency surgery at Royal Brisbane and Women's Hospital, and is understood to be in a stable condition.

The offender was described as being white and in his 20s.

A police spokesman said it was unclear if the victim was homeless.