Earlier on Friday the national team, which takes on Switzerland in a last 16 World Cup clash next week, said that they would pay the 120,000 Swedish crowns ($13,415.92) the city normally charges to stage an event at Kungstradgarden.
"We are not accepting payment as we want to help in this case," Stockholm City Head of Events Roger Ticolau said.
The payment is normally used to cover the cost of equipment and personnel at the outdoor venue, which recently hosted the homecoming of the national ice hockey team that won the World Ice Hockey Championships in Denmark.
The anti-racism demonstration, which almost 10,000 people said they would attend on Facebook, was due to be held at Sergels Torg in the city centre on Friday evening.
But police denied permission for it to go ahead, saying building work in the area would make it unsafe for a large gathering.
The organisers were told it would be better to move the event to nearby Kungstradgarden, but the price tag of 120,000 Swedish crowns to hold it there was way out of their league -- until the players stepped in and said they would foot the bill if necessary.
"I got a phone call from (Swedish FA general secretary) Hakan Sjostrand, and he said that the players had heard about this, they had a conversation about it, and decided they wanted to help," organiser Shanga Aziz told Reuters by telephone.
Aziz is part of a group called Locker Room Talk, whose goal is to improve the atmosphere in sport by educating young players about the toxic environment created by racist, homophobic and misogynistic speech in the dressing room.
Sweden winger Durmaz conceded the stoppage-time free kick that led to Germany's Toni Kroos scoring a stunning goal for a 2-1 win in Sochi on Saturday, and it led to hundreds of racist and threatening comments being left on his Instagram account.
The Swedes, who came out and backed their team mate, bounced back to beat Mexico 3-0 and win Group F, while the Germans were eliminated after a shock 2-0 loss to South Korea.
"We hope as many as possible show up. We want to stand up for everyone's equal rights and show that racism is never OK, that we should be able to be ourselves without this hate and these threats being made," Aziz told Reuters.
(Reporting by Philip O'Connor; Editing by Hugh Lawson and Christian Radnedge)
