A distress call was received at around 03:30 local time (02:30 GMT) on Monday, which triggered a major rescue operation which is currently underway.
Jonas Franzen, a spokesman for the Swedish Maritime Authority, told the BBC that the rescue team heard screams coming from the near freezing water.
"We have not found anyone yet," Franzen said.
He said that divers have been sent out to join the rescue efforts, along with two helicopters and several boats from Sweden and Denmark .
One of the ships involved is the Scot Carrier – a UK-flagged and Inverness-registered cargo ship that was heading to Montrose, on the east coast of Scotland.
The other cargo ship that overturned is ‘the Karin Hoej’, which is registered in Denmark.
The two people believed to be missing were the only people on board ‘the Karin Hoej’.
All crew on the Scot Carrier are said to be safe and well.
The team aboard the Scot Carrier is reportedly attempting to turn the Danish ship upright and return it to a nearby port.
As of yet, the cause of the crash is unknown.
Sweden’s Coastguard has said that an investigation has been launched, and that the possibility of “gross negligence” causing the crash will be considered.
Danish authorities have confirmed that the captain of the Scot Carrier has submitted to an alcohol test, as part of standard procedure.