Officers from West Midlands Police say the man was arrested on suspicion of wounding on Saturday following attacks around Ladypool Road, Sparkbrook.
He has since been released pending further enquiries.
A West Midlands Police spokesperson said: "A 27-year-old man was arrested on suspicion of wounding yesterday. Following questioning he has been bailed pending further investigation.
"The victim remains in a critical condition in hospital."
Police said a man attended hospital at around 3.10am on Saturday with "gunshot wounds to the neck", and remains there in a critical condition.
Officers received two reports violence in the early hours of Saturday - one in Ladypool Road in the Sparkbrook area of the city just after 2.30am, and another in Walford Road, Birmingham, at around 2.45am.
After no injuries were reported to police at Ladypool Road, officers found a man who had been shot in the leg at the second incident.
He has been taken to hospital where his wounds are said to not be life-threatening.
Officers have not ruled out the possibility the two incidents are linked.
Detective Inspector Megan Stokes said: "We were initially called to a report of a disorder in Ladypool Road, Birmingham at just after 2.30am today.
"Officers attended and it was reported that a gunshot had been heard but no one reported any injuries to us.
“Our teams are working hard to establish exactly what has happened and we are keeping an open mind as to whether these incidents are linked."