Officers carried out raids in three towns on Tuesday morning, and said those in custody were suspected of planning Islamist attacks in Sweden.
Police in Sweden have arrested five people suspected of conspiracy to commit terrorist offences.
Raids were carried out in the towns of Eskiltuna and Strängnäs, west of Stockholm; and Linköping, south of the capital, on Tuesday morning, with the Swedish Security Service Sapo saying they undertook an intelligence-driven investigation ahead of the arrests.
Authorities say those arrested have "international links to violent Islamist extremism."
"The Security Service often needs to intervene at an early stage to avert a threat. We cannot wait for a crime to be completed before we act," says Susanna Trehörning, Deputy Head of Counterterrorism at Sapo.
"The current case is one of several that the Swedish Security Service has been working on since the protests directed at Sweden in connection with the high-profile Koran burning in January, where international calls for attacks have been made," Trehörning adds.
Police say they don't think a terrorist act was imminent.
What was behind the Quran-burnings in Sweden?
In January, a far-right activist first burned a copy of the Mulsim holy book outside a mosque in Copenhagen, and then a few days later replicated the stunt in front of the Turkish Embassy in Stockholm.
Rasmus Paludan, who holds dual Danish and Swedish nationality, sparked protests across the Middle East and Asia, with Turkey branding his actions a "hate crime"
The Quran is regarded as the word of God in Islam, and any attack on it is deeply offensive to Muslims.
Part of the outrage was because Swedish authorities apparently allowed Paludan to burn the Quran while the police and media looked on.
However, the Scandinavian country has very strong free speech laws, and while senior politicians condemned the act, they stressed that they could not prevent it from happening due to freedom of expression laws.
In February, police told Euronews they had turned down another request to hold a rally where organisers planned to burn a Quran.
Previously, Sapo warned that the threat of attacks in Sweden had increased in the weeks after Paludan's stunt.
The agency noted that international reactions to the events outside the embassy in January "have been extensive” and "the assessment is that the security situation has deteriorated.”
"Sweden is judged to be in greater focus than before for violent Islamism globally," Sapo said at the time.
The security agency, however, did not change Sweden's terror threat level, which already stood at three on a five-point scale.