Pupils have been told kickabouts and all other ball games are off limits at playtime during the tournament.
Instead, staff at Hall Road Primary, in Orchard Park, Hull, hope pupils will skip and play with outdoor chess sets.
Deputy head teacher Kristina Frary said the ban was needed to prevent injuries and allow staff to get on with teaching.
She said: “Passions are running high, especially with the Euro 2012 football tournament. Potentially, that’s why children are wound-up.
“We have had a sequence of fall-outs and they were all centred around football.
“It was only a small number of incidents - maybe half a dozen - but we have decided to have a break.”
Mrs Frary said as well as playground spats, pupils were being overzealous in their tackles after watching their footballing heroes in action in Poland and the Ukraine.
She said: “Children are really into their games and, just like the professionals, they will sometimes misinterpret tackles and perhaps reply in a way that would get them the red card if it happened during a real game.
“It was causing problems. Come the end of break-time, children were still upset and it was spilling into their lessons.
“Teachers ended up spending valuable lesson time sorting out problems.”
Head teacher Caroline Holliday said the ban has been imposed to show children the consequences of bad behaviour.
She said: “Children need a period to reflect and take responsibility for their actions.
“This past week, since the ban, we have noticed older pupils taking better care of the younger ones and enjoying other sports and pastimes.”
Orchard Park ward councillor Julie Conner said she was disappointed to hear about the football ban, but would not condemn the school.
She said: “It is sad the school has had to take this step. Children enjoy letting off steam on the playing fields during lunch and break-time.
“It is especially sad that they can’t do this during Euro 2012. With the arrival of the Olympic Torch in Hull this week too, the city has become very sports orientated.”
Ms Conner said she had not heard about the ban but said the school must have had its reasons.
She said: “Clearly, there must have been several situations at the school that has resulted in this.”
Mrs Frary said football and other ball games are still being enjoyed by pupils during PE and games lessons.
She said: “Our Year 5 and 6 classes have just come second in a football tournament held at Kelvin Hall and this week Year 3 will be taking part in a competition at the University of Hull.”
Mrs Frary said Hull City is also running football classes for its pupils.
She said: “We have them coming to do a sponsored penalty kick. Next week, we have a full week of sport, featuring a range of sport, not just football, such as basketball and gymnastics.
“This was praised by Ofsted during our last inspections. They thought it was amazing.”
Mrs Frary stressed the children are still letting off steam during breaks.
She said: “We have other playground activities for the children, such as skipping, big chess sets and hoola hoops.
“These seem to be very popular with them.”
She said the school had not received any complaints from parents about the ban.