"We are all worried, we are scared to death," one mother, who did not want to be identified, told news agency TT.
The children and parents approached the school cautiously on Monday morning. Classes are going on as scheduled, but it is far from a normal day.
Police stand guard outside the school but the police at the school would not say for how long the school will receive the extra protection.
One father of a child at the school told TT that he was a student at the school in the 1970s and thinks that the security has gotten worse since then.
"When I was growing up there were guards outside the school every day," he said, choosing to remain anonymous.
Stockholm police say that they are "taking measures" for security and are continuously assessing the situation.
The Jewish middle school within Vasa Real in Stockholm is also continuing with classes, with heightened security.
John Gradowski from the Jewish community in Stockholm told Radio Sweden more resources have been allocated by the government to protect the community, but that they are all concerned at the latest developments in Denmark.
"Sweden looks upon itself as a country where this kind of thing couldn't happen", he says, "which is stupid, because we had the suicide bomber a couple of years ago, Olof Palme was murdered, Anna Lindh was murdered, things have been happening here as well. There is an innocence, but I think people are starting to wake up now."
Minister of the Interior Anders Ygeman told Swedish Radio News that the threat against Sweden's Jewish minority is being taken with the utmost seriousness.
"We take their concern seriously, and we will do everything we can to make sure they can practice their religion and live freely in Swedish society like everyone else," Ygeman said.
Ygeman also said that there have been recent visible examples demonstrating just how seriously they take the threat.
"An example is the more visible police presence and observation. Another example is the continued police work to uncover threats. But," he said, "it is also about an open and democratic society, where we must start a conversation about anti-semitism."