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."

Another car ploughed into the parked vehicles in Emlyn Street in Talywain near Pontypool on Sunday.
A 45-year-old woman has been charged with aggravated taking of a vehicle, driving without a licence and insurance, theft and possession of a class C drug.
She has also been bailed on suspicion of driving while unfit through drugs.
Gwent Police have talked to some witnesses but have appealed for more people who saw the incident at 15:50 BST to contact them on 101.
A 19-year-old man was stabbed in the chest during a brawl involving up to 30 men in Birmingham, say police.
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Motorists are counting the cost after a trail of car damage was left on a street in Torfaen.