Suffolk Police confirmed they were investigating the incident at Heath Hatcheries in Mildenhall that happened on the night of Friday, April 19.
They said a number of unknown persons cut the fence to access the property, and then broke into the cages "allowing thousands of breeding stock pheasants to escape."
The Animal Liberation Front (ALF) claimed responsibility for the raid and said on Facebook they put grain down in a clear path to direct the birds towards a nearby forest and away from the road.
In the post, they said: "With game farms being targeted across the country, many shoots may well go out of business this year.
"We will continue to dismantle the shooting industry, farm by farm, shoot by shoot, until the end."
The Countryside Alliance said it was "completely unacceptable" and added, "farmers should not have to live in fear".
Tim Bonner, the chief executive of Countryside Alliance told The Times: "This latest attack on a game farm by animal rights extremists is completely unacceptable.
"By releasing birds without making provision for them to adapt to the wild many of them will die as a result of these thoughtless and ignorant acts."
The AFL has claimed responsibility for similar incidents in March where nearly 5,000 pheasants were released from a farm in Wiltshire and around 1,000 escaped from a farm in Bodmin, Cornwall.
Police have appealed for witnesses, anyone with information should contact Suffolk police quoting crime reference 37/22245/19 or call Crimestoppers on 0800 555 111.