The rhea - nicknamed Chris by officers - was seen near the village of Thriplow over the festive weekend.
There have been sightings in the villages of Foxton, Newton and Fowlmere.
The bird, which originates in South America, can reach running speeds of up to 40mph (64km/h).
RSPCA guidance say rheas "have the potential to be dangerous as they are strong, fast and have sharp claws" and says people should keep away and call the charity if they see one.
It is not known whether the bird was being kept in the area.
It is not the first time a rhea has launched a bid for freedom locally.
In January, police were called when one of the giant birds emerged from a children's playing field in Terrington St Clement, near Wisbech.
And in May 2015, a rhea that escaped from a smallholding was shot at Barkway Park Golf Club, near Royston in Hertfordshire, by a gamekeeper.
A 6ft flightless bird spotted roaming on Cambridgeshire farmland on Christmas Day is still on the loose, according to police.