The reservation system has been down all morning and as January 1st is a national holiday the phone lines are also closed.
Along with the SJ website the post service (Posten) along with the Systembolaget and Stockholm's local transport websites are all affected by the cable fire at IT company Evry.
"You can't buy tickets through the website. Right now we can't made a prediction for when the error will be rectified," Mårten Dunér, press spokesperson for SJ told Dagens Nyheter.
He added that it was "most likely" that passengers would be able to buy tickets on board trains which are running today.
The problem was discovered shortly after midnight when the servers were found not to be working properly. A fire at a transformer station had affected the electricity supply but the premises where the servers are located was intact.
A spokesperson for SJ said that only the online booking system was affected and that trains scheduled to operate on New Year's Day were running as normal.
"We only have access to social media where we have informed passengers that they can get on the train they want to travel," said Ulf Wallin of SJ's press department to the TT news agency.
Wallin also said that the fire at the IT company was "extensive" and that there was a risk that it could drag on.
In addition to the national rail operator the websites for state controlled liquor store Systembolaget, the national post office and Stockholm's public transport (SL) have also been shut down.
"The latest information I have received is that that they are working frantically to fix the problem," said Henrik Palmér of the SL press office.
UPDATE: As of January 2, 2014, the system is up and running again.