Following the destruction of two camps last year, the lack of suitable shelter has intensified, according to the newspaper.
The principal and janitor of the school now often find themselves starting their day by waking migrants sleeping in tents in the school's yard.
The situation is “clearly a cause for concern,” Principal Christina Hagelin told Sydsvenskan.
The school saw an increase in the number of people camping in its yard during the autumn, at first in sleeping bags under the open sky, and then sometimes using tents as the weather got colder, says the report.
A number of students witnessed police asking two people to remove their tents and leave the school yard on Wednesday.
“I think it was a neighbour that called (the police). But this is a recurring concern,” Hagelin told Sydsvenskan.
“It is tragic that it has to be like this,” added the principal.
A camp for EU migrants in Malmö's Pildammsparken was torn down in the spring of 2015. A second camp, near Industrigatan in the centre of the city, was also removed in November that year.
Prior to the demolitions, a number of conflicts emerged when residents in the areas around the camps complained about issues such as littering. Groups in support of the EU migrants were also formed.
The city of Malmö has around 40 beds for homeless people.
“There has been much more demand this year than last. We have basically been fully occupied since day one,” Reverend Andreas Wessmann of the Pingskyrkan church, which provides the overnight accommodation for the homeless, told Sydsvenskan.
Pierre Douhan of Malmö's municipal police confirmed that camping at the school was forbidden, but that the situation was not straightforward to resolve.
“Camping in the city is forbidden, but the problem is bigger than that. These are people who are vulnerable in many ways,” Douhan said to Sydsvenskan.