Officers discovered the injured teenager after being called to Graiseley Street in the Pennfields area of the city just before 8pm on Monday night, West Midlands Police said.
He was taken to hospital and remains in a serious condition.
Two boys aged 15 and 17 have since been arrested on suspicion of attempted murder while a 20-year-old man has been detained on suspicion of assault.
All three remain in police custody while an investigation into the circumstances is continuing.
Inspector Ade George, of West Midlands Police, said: "I am appealing directly to anyone who was in the area and saw what happened to contact us if they have not already done so.
"No matter how insignificant you feel the information may be, it could really help with our investigation as we continue to follow forensic and CCTV inquiries."