DBU confirmed on Wednesday that its negotiations with the Danish Football Players' Association have broken down.
In a press statement, DBU wrote that the cancellation was a result of players “not reporting for training on Monday or Tuesday.”
“It is a historically bad day for the women's team and for Danish football overall,” DBU senior vice-president Kim Hallberg said in a press statement published on the governing body's website.
“It is regrettable but also grotesque that we are in a situation where players will not report for major international matches, even though we have offered better terms and invited them to new negotiations after the matches,” Hallberg added.
“We have now announced that the players' absence has resulted in the cancellation of the match on Friday. That is naturally very disappointing,” DBU press officer Jacob Wadland told broadcaster DR.
“We have informed the Swedes that we will not be able to provide a team,” he said.
DBU and the players' association have been in negotiations over pay since November 2016.
DBU says it has offered to increase the investment in the women's team by two million kroner (270,000 euros) per year, from 2.6 million to 4.6 million kroner.
The cash injection was reportedly offered for investment in higher salaries and bonuses for players and strengthening auxiliary staff.
Currently, players receive about 14,000 kroner (1,880 euros) on average per month. The wages of their male counterparts have not been disclosed.
The men's team offered to give up their 500,000 kroner (67,000 euros) annual bonus for the women, in an initiative echoing an agreement recently reached by Norway's national football teams, but this was rejected.
A key factor earlier in the debate has been whether the agreement between DBU and the Danish Football Players' Association stipulates that the players are employees and DBU their employers.
The two parties interpret the terms of the current agreement differently, with the players' union seeing the players as employees – giving the players certain rights, including equal pay.
But DBU does not see this as the case, and wants future agreements to define players as not being employees of DBU.
“This is not just about money, but also about principles. We are getting there economically speaking and can perhaps agree with each other. We recognise that, but do not want to be employers. That must be clearly expressed in the new agreement,” DBU head of communication Jakob Høyer told Ritzau last month.
Consequences of the Danish cancellation in the form of punishments from either FIFA or UEFA are currently unclear, with neither body having taken an official stance on the issue before the potential situation became reality.
“There is no precedent, and it is [FIFA and UEFA's] independent disciplinary body that will take that decision,” Hallberg said to DR.
Denmark officially has until 12pm on Thursday to submit a squad for the tie.
DBU's Swedish counterparts, Sveriges Fodboldforbund (SvFF) called the situation “peculiar”.
“This is a peculiar situation that we have not experienced before,” SvFF communications officer Andreas Jansson told DR.
SvFF has requested advice from UEFA over the issue, Jansson said.
“We will not speculate on the consequences of this issue until we have received advice from UEFA on what this means,” he told DR.
The Swedish team was meanwhile continuing its preparations for the match, he added, with approximately 8,000 tickets for the match in Gothenburg are reported to have been sold.
Denmark's women's national team reached the final of this summer's UEFA Euro 2017 championships in the Netherlands, where they lost to the hosts.