Up to 25,000 Swedish supporters visited Kiev where their team played all of its three matches. They were the largest group of fans and generally left a favourable impression on locals, who are keen for them to return as tourists.
City officials on Saturday unveiled the sculpture on the picturesque Trukhaniv Island in the Dniepr River where many Swedish fans camped out in tents.
The sculpture is topped with Viking horns and depicts the number "12" in Sweden's national colours of blue and yellow. Fans are sometimes described as the "number 12" player in a team.
Nevertheless some Swedish fans complained the figures also brought back bad memories of the first game of the championship when Sweden lost 1:2 to Ukraine.
"I see the numbers. It is a little sad that we can see the result of the match," said the former leader of the Swedish fan camp Ola Sjostedt, who flew in specially for the opening, wearing a bright-yellow T-shirt.
The city authorities hope the new memorial will encourage Swedish fans to make a return visit to Kiev.
"Every Swede who comes to Ukraine will want to look at this monument because it is a sign of friendship," said Kiev city manager Olexander Popov.
Both Ukraine and Sweden exited at the group stage of the championship, which was the most important sporting event ever hosted by Ukraine.