“We are closing airspace sectors one by one and we are following the ash cloud … It’s coming from the northwest” of Sweden, LFV spokesman Carl Felling told AFP.
“We will close Malmö and the south parts of Sweden at 4pm, and everything except the Baltic Sea and the island of Gotland will close by 6pm,” he said.
LFV added that it was too early too say when Swedish airspace could be reopened.
Scandinavian airline SAS cancelled 635 flights, or almost three quarters of its daily air traffic, on Thursday because of ash from a volcano eruption in Iceland, a company spokeswoman said.
“So far, we have cancelled 635 flights out of 870 daily. The ones flying were mostly in Denmark and Sweden, while there was barely any traffic in Norway,” Elisabeth Manzi said.
Budget airline Ryanair has already cancelled all flights to and from Sweden from 11.30am on Thursday, with volcanic ash also leading to airport closures across the country.
Earlier, the Civil Aviation Authority closed the skies in northern Sweden as a cloud of ash caused interference in Swedish aerospace.
The authority introduced the flight ban from 10pm on Wednesday for all air space north of Luleå but expanded the area down to Skellefteå at around 6am on Thursday.
The measures come amid fears that the clouds of ash could damage aircraft engines.
The volcanic eruption occurred on Wednesday under a glacier in the Eyjafjallajökull area of Iceland and was the second eruption in the country in the space of a month.
The eruption sent a huge ash cloud across Northern Europe, prompting airspace closure in Britain, Ireland, the Netherlands, Belgium and hundreds of flight cancellations worldwide.
Icelandic airports, however, reported no problems.
“The wind is blowing the ash to the east,” Hjordis Gudmundsdottir of the Icelandic Airport Authority told AFP, adding: “It’s amazing really.”