According to Swedish radio station, P4, the graffiti was painted on the centre circle in the early hours of Saturday morning.
As well as the painting of the Nazi graffiti the pitch's artificial turf was dug up in places.
According to a football club spokesman, Christian Nyreröd, the reaction to the graffiti will prove positive.
“I think it affects positively the tournament; I think people will want to show their support (for the refugees).”
In April five boys in southern Sweden were charged with inciting racial hatred after they were found raising their arms in what appeared to be a Nazi salute while posing for a school yearbook photo.
In the same month residents of Vetlanda in southern Sweden were shocked to see a Nazi flag flying from one of the official flagpoles next to the town hall.
However, in May, a new report found that Swedish neo-Nazi groups were less active in 2015.