The arrest was made on Monday night, after an incident reportedly involving a six-inch blade that took place in Castle Vale earlier that morning.
Officers confirmed that a "juvenile male was booked into custody".
They also released an image of the alleged weapon in question.
Erdington Police published the following statement on social media just after midnight on Tuesday: "Tyburn officers have arrested an eleven (yes, 11) year old male in Erdington tonight after he allegedly intimidated another child with a 6-inch knife in Castle Vale this morning.
"Juvenile male booked into custody."
It comes alongside news that the West Midlands has been chosen to host a pilot for Serious Violence Reduction Orders (SVROs), which will give police powers to stop and search criminals with knife offences and gang members without reason.
The two-year scheme starts in April and comes as the region continues to face soaring levels of knife crime and violence.