The injured man went to hospital Friday evening and is in a critical but stable condition following surgery, a force spokesman said.
Officers said 15 minutes earlier police received "numerous calls" to Malvern Hill Road, Nechells, where the stabbing was believed to have happened.
Two men aged 20 are being questioned on suspicion of violent disorder.
Det Sgt Adam Hicklin said: "We know this was a targeted stabbing but at the moment we're not clear on the motive behind the attack."
A 19-year-old man was stabbed in the chest during a brawl involving up to 30 men in Birmingham, say police.