A total of 35 firefighters were sent to the scene at Five Ways Tower at 4.30pm on Saturday to the blaze in the plant room.
A spokeswoman for West Midlands Fire Service said: "We were called just after 4.30pm and sent seven fire engines to a fire in the plant room.
"A member of the public called and said there could be squatters in the building but everyone was accounted for.
"The fire investigation team did attend and said it was a deliberate ignition."
Fire officer Lee Baker tweeted saying: "Five Ways Tower, Birmingham on 21st floor of void High Rise. Crews ran hose and equipment up 21 floors due to no dry riser and water supply."