Kiwi's owners called the fire service in a "very distressed condition" when the bird became trapped as it climbed.
Watch Commander Desmond Lloyd from Oldbury fire station said his "fat fingers" enabled him to bend the bars of the cage to free the parrot.
He said it was the first time in his 29-year career he had heard of crews rescuing a parrot from its cage.
Mr Lloyd said: "We've got them down from trees. But not usually from cages.
"Luckily I have fat fingers and managed to bend the bars to let Kiwi pull his head out."
A parrot was rescued from its own cage by a firefighter after getting its head wedged between the bars.