Police said the American Harris hawk, named Rufus, was taken together with its cage and handling glove overnight between Thursday and Friday from a car park in Wimbledon.
Officers said Rufus was a family pet and described his owners as very "distressed" over the theft.
Police said the working bird of prey deters pigeons by its presence at the All England Lawn Tennis Club.
For the past four years, the hawk has spent every morning of the Championships scaring pigeons away from the hallowed grass.
Rufus usually patrols between 05:30 and 09:00 (local time) before the public arrives.
A spokesman said that one of Rufus's "pals", Hector, had been drafted in so there was no increased risk of pigeons becoming a nuisance on Centre Court.
Avian celebrity Rufus is something of a Wimbledon fixture with his own Facebook page and Twitter account with 257 followers, the BBC reported.
Owner and handler Imogen Davies, of Avian Environmental Consultants, which supplies birds of prey to control birds, said: "It's hard to get your head around. We just want to know he's ok."
Asked about the value of the bird, she said: "It would cost about 250 pounds to buy a bird like Rufus but you couldn't put a value on him to us."
She said the roof of Centre Court was particularly appealing to pigeons but Rufus's presence immediately scared the birds away and stopped them roosting.
