A 2010 report said around 200 extremists with terrorist sympathies were living in the country.
But this has now risen to the thousands just seven years later.
Säpo chief Anders Thornberg said: “We would say that it has gone from hundreds to thousands now.”
And he added the vast majority of radicals in the country support violent Islamist ideologies.
He said: “We have never seen anything like it before.
“This is the ‘new normal’. It is an historic challenge that extremist circles are growing.
“We used to have different circles. We had radicalised people from North Africa, the Middle East and Somalia, but they were all separate.”
However he stressed that the security service believe most of them do not have the ability to carry out a terror attack in Europe.
Säpo receives about 6,000 intelligence tip offs per month regarding terrorist activities and extremism, up from around 2,000 a month in 2012.
And in 2012, the intelligence agency estimated that about 300 Swedes had left the country to join ISIS in Syria and Iraq.
Säpo is expected to release a more accurate figure on the number of extremists in the country in the coming days.
Terror expert Magnus Ranstorp of the Swedish Defence University told The Local the new figures were expected.
He said: ”Those of us working in the field of counter-terrorism are not surprised, it has been in the making for some time, it didn’t just appear.
“When IS declared the caliphate, that was the genie out of the bottle.”
He added: “It is a development we’re seeing in general, of course it’s worse in bigger countries.
“In the UK there are 23,000 extremists, in Belgium there are 18,000, in France 17,000. Not everyone is equally dangerous, but it only takes a small number of people.”
Sweden was the scene of a deadly terrorist attack in Stockholm in April, which was claimed by the Islamic State.
The man hijacked a delivery truck and ran over pedestrians, killing five and injuring 15 after mounting the pavement outside a busy shopping centre.