The lynching took place in the Upazila's Prembag village around 4 am on Monday, said Abhaynagar Police OC Tajul Islam.
The dead men were aged between 35 and 45 years but no further details about their identities could be known immediately.
Police, citing the accounts of a few locals, said a few men in the neighbouring Gaidgachi village allegedly stole three cattle from the home of one Khorshed Alam and loaded the livestock onto a pick-up truck in the early hours of Monday.
Villagers subsequently set out to chase down the suspects, who entered the neighbouring Abhaynagar village to evade them, said OC Tajul.
"But the Gaidchari residents caught them at a school field next to the Prembag rail crossing and began beating them up. Two of them died on the scene while the other man was declared dead after being taken to Abhaynagar Upazila Health Complex."
Police recovered the bodies from the scene and seized the vehicle used for the theft, said the OC. The three cattle were also rescued.