The food was stolen from the Saint Anthony of Padua Church Saturday, The Boston Globe reported.
Along with the turkeys, the thieves took eggs and 150 pounds of cheese, police said. The food was worth about $600.
The community is trying to help the church rebound from the loss, but there is still a need for food for Thanksgiving, Joel Cosmo, Saint Anthony's sexton, said.
"We serve up to 700 families every two weeks," Cosmo told the newspaper. "It's important for us to make sure our supply is not too drained, especially this time of year when the need is higher than any other time."
The thieves damaged an industrial refrigerator where the food was kept, Cosmo said.
"They really did some extensive damage," he said.