All three men are Swedish citizens of Somali origin.
Prosecutor Ronnie Jacobsson confirmed that one of the men, a 42-year-old, was the same man who had a map of artist Lars Vilks' house confiscated by police late last year.
But Säpo stressed that the map had nothing to do with Thursday's arrests. Artist Lars Vilks outraged sections of the Muslim world last year with a series of caricatures of the Islamic prophet Muhammad.
"The men were arrested at different addresses in the Stockholm region," Säpo spokesman Jakob Larsson told the TT news agency.
According to the prosecutor, the court will make a decision tomorrow on whether to remand the suspects in custody.
Norway's security service PTS also arrested three men in Oslo on Thursday morning on similar charges in a raid coordinated with their Swedish counterparts.
The Oslo arrests followed a lengthy investigation carried out by Oslo police in cooperation with the police financial crimes unit.
The three men apprehended in Norway are suspected of financing acts of terrorism abroad.
The arrests were described by police in Oslo as undramatic.
Terrorist financing is viewed as a growing problem in many European countries. The Nordic region in particular has been described as a sanctuary for terrorist groups, where they can plan acts of terrorism with little risk of detection.
Säpo has previously referred to Sweden as a base for "recruitment, logistical support and financing" of terrorism.
At least 20 Swedes have been arrested globally on terror charges since 2001, many with suspected links to extreme Islamist organizations.
Most recently, a 23-year-old Swedish national was arrested in France on February 1st suspected of fighting with Somalia's Islamic courts.
Four Swedes were also arrested and imprisoned in Ethiopia when Somalia's Islamist movement was driven back by government forces in 2006.
Only a few cases have led to convictions however. In 2005, two Iraqi Kurds were jailed and deported by Sweden's Court of Appeal for financing terrorism.
The men, one of whom was an imam, had sent $148,000 to the Ansar al-Islam terrorist movement in northern Iraq.