A gunman allegedly shot dead three people after a drunken argument in the queue at a McDonald's all-night drive-through in Finland turned deadly, police said.

Police were called to the burger bar in Porvoo, just north of Helsinki, at around 2 a.m. after shots were fired. A man has been arrested after fleeing the scene, they said.

"What we know is that there were three cars in a row waiting to be served at the McDonald's hamburger restaurant," investigator Peter Fagerholm of the local police in Porvoo said.

"They started to argue, and started a little to fight and that led to the shooting... One of the people involved took out a handgun and shot these three people," he said.

Two men in an open convertible were killed on the spot while a third man who was in the same car died of his injuries in hospital Tuesday afternoon.

"There were two people shot in the head and one in the chest at very close range," Mr Fagerholm said.

A pregnant woman and her boyfriend were also in the car but had escaped unharmed. It remained unclear what had set off the row, he said.

"It appears it was basically an argument between drunk people. Nothing serious ... Nobody could have expected that one of them would take a handgun out and start shooting these people," he said, add-ing that the shooter and victims had not known each other.

"It is unbelievable that these people were just going for a hamburger and ... now we have three people dead," he said.