The Mounties say the rodent had been gnawing at the large tree next to Highway 16 at Priest's Point, near Souris, before it fell at about 2 p.m.
The driver told investigators he saw the tree falling onto the roadway but he was unable to avoid it as it crashed down onto his vehicle.
The couple and their two infant children weren't injured but the Toyota they were in sustained significant damage to the roof, windshield, and to a cargo box.
Police say when they examined the tree they found it and several other nearby trees had been chewed by the beaver, and arrangements were made to have the damaged trees taken down.
The vehicle has been taken to a body shop for repair, and police say "the beaver is still at large."