"It looks like it will come in over Swedish territory during the latter part of Tuesday, but probably with a very low concentration," said Gustav Åström at Sweden's Meteorological Institute (SMHI) to the TT news agency on Monday afternoon.
The eruption of the Grimsvötn volcano in south-east Iceland is reported to be more extensive than the eruption of the Eyjafjallajökull volcano in 2010 which caused weeks of air travel chaos across Europe.
Sweden's Civil Aviation Administration (Luftfartsverket - LFV) meanwhile confirmed on Monday morning that aside from flights to Iceland, Swedish air traffic was operating normally.
"The ash from the Grimsvötn volcano is not affecting Swedish air traffic as the situation is now. The Swedish Transport Agency is the authority which would decide on restrictions. The Civil Aviation Administration is following developments," LFV said in a statement on its webpage on Monday morning.
Swedavia, the firm which operates 14 of Sweden's largest airports, confirmed on Monday that operations are as normal.
There are nine appointed "Volcanic Ash Advisory Centres" worldwide which develop forecasts and issue warnings. The Swedish authorities follow their lead with support from SMHI.
According to the UK Met Office the ash cloud, which currently covers Iceland and parts of eastern Greenland, is spreading and is set to reach the British Isles later on Monday.
The cloud is expected to reach northern Norway around lunchtime and spread across northern Russia during the afternoon, carrying with it the prospect of further air travel disruption.
While there is a great deal of uncertainty, some experts fear that the massive plumes of ash which continue unabated from Grimsvötn, Iceland's most active volcano, could prompt the same chaos which gripped Europe last April/May.
"If it continues with the same intensity then it is very possible that there will be the same chaos as last year," seismologist Reynir Bödvarsson told Sveriges Radio (SR).
Sweden's airspace was closed on April 15th, 2010 as winds pushed ash clouds from the Eyjafjallajökull volcano across the country. The disruption lasted several weeks with thousands of people stranded across Europe as airports remained closed.
The Eyjafjallajökull ash cloud and subsequent disruption led to airlines incurring significant financial costs and Scandinavian airline SAS was among the carriers which cited the problems as a contributing factor to poor 2010 results.
After the experience of 2010 the European aviation industry is reported to be well-prepared to manage the situation.
Research has been completed, routines introduced and the industry works together to identify which flight zones need to be closed.
"Last year's ash cloud cost SAS 700 million kronor ($110 million), I find it hard to see that this cloud will be as expensive," said SAS analyst Jacob Pedersen at Danish Sydbank.