The man was taken to hospital with an arm injury. It is not believed to be life threatening, West Midlands Police said.
Six people four men and two women were arrested for firearms offences at a property in Shepherds Gardens, Edgbaston, at around 5am.
The men aged 21, 35, 45 and 52 and women aged 59 and 64 all from Birmingham have been arrested on suspicion of firearms offences and remain in police custody.
A firearm was recovered by police and has been seized for forensic examination.
Police had entered the property looking for a man wanted in connection with a firearms offence.
The incident has been referred to the Independent Office for Police Conduct. Police said inquiries are at an early stage and investigations are continuing.
Police issued a statement to confirm the arrests are not connected to conference.