The Swedish requirement for ID checks at the border between the two countries has resulted in 10,000 people being turned away from the ferry, that connects the Danish town of Helsingør with Helsingborg in Sweden.
Almost all of the rejections were due to normal travellers forgetting to bring their papers, reports Danish broadcaster DR.
ID and border checks were introduced on 4th January this year in an effort to prevent asylum seeker without papers from travelling to Sweden to seek asylum.
Only 200 hundred of the 10,000 recorded refusals during 2016 were potential asylum seekers, according to the report.
"The majority of the people we refuse boarding are Scandinavian citizens, mostly Swedes. We're obviously all used to travelling in a region where mobility is in flow," Henrik Rørbæk, administrative director of HH Ferries, told DR.
"It is a big procedure for the sake of relatively small figures. And in general, the flow of asylum seekers up here has not been very great. It also shouldn't be any secret that this is costing us large amounts each month," Rørbæk continued.
Rørbæk told DR that the ID checks cost the company three million Swedish kronor ($325,000) every month.
Over three million passengers passed through HH's ID checks in 2016, reports DR.
The company must pay fines of up to 50,000 kronor ($5,400) every time a passenger is stopped by Swedish border control without ID.
"Most people are understanding, but many others blame us for not being able to travel. So if I could have a little Christmas present, it would be that we found more convenient ways in which to maintain the border checks, so that they don't disadvantage individual travellers," said Rørbæk.
The director added that his company did not take any political position with regard to the ID checks.
Opposition party Enhedslisten (The Red-Green Alliance) decried the ID checks as a 'waste of resources'.
"These figures show that this border control is a bit silly. It does not stop criminals or asylum seekers, and in practice just cost money and inconveniences people," legal spokesperson Pernille Skipper told DR.
But Integration Minister Inger Støjberg told the broadcaster that she was not about to reconsider border control.
"We know that things can change very quickly and that a large number of asylum seekers who possibly want to travel on to Sweden might come here, and get stuck here, so as long as the Swedes maintain their ID checks, I see no reason why we should lift our border control," Støjberg said.
Martin Henriksen of the anti-immigration Danish People's Party told DR that if it was up to his party, it would "always be necessary to show a passport to enter Denmark. Even for people coming from Sweden."