They evacuated the 21-storey block of flats.
Then a police sniper abseiled down the side of the building armed with a tranquiliser gun.
With the aid of a police camera, which was keeping an eye on the tiger, he managed to sedate the creature.
"I saw him eye-to-eye. He charged twice and I shot him," the sniper was reported as saying.
A search of the flat revealed that the owner was also keeping a 1.5m alligator on the premises.
The creatures have been taken to an animal care centre.
Their owner is facing police charges for keeping them.