Dan Eliasson, who has headed the agency since 2018, asked the government to reassign him and the government was expected to make a decision shortly, according to a statement from the agency.
The row started after the Eliasson travelled to the Canaries to spend Christmas with his daughter, a resident of the islands, which are located off north Africa.
The daily newspaper Expressen reported that Eliasson had flown out a little over a week after the government had recommended people not to travel overseas unless “necessary”.
Eliasson defended the visit telling the paper, “I have refrained from a great deal of trips during this pandemic but this one I thought was necessary.”
However, the trip provoked widespread anger and led to several opposition politicians calling for his resignation.
Eliasson said his decision to resign was motivated by those reactions and the impact they would have on the work of the agency. He wanted MSB to “have best conditions to do its important mission”, he said.
“The important thing isn’t me as a person. The important thing is how we as a society handle the pandemic and that all focus is on that incredibly important task.”
Sweden made world headlines for its decision to combat the coronavirus with mostly non-coercive measures rather than enforcing the lockdowns seen across Europe.
Officials have repeatedly urged people to take responsibility, but over the holidays several reports of officials not heeding their own advice emerged, angering sections of the public.
Several politicians appeared to be ignoring guidelines to avoid crowds and not to travel, even if they were not breaking the law.
Prime Minister Stefan Lofven was photographed visiting a watch store in central Stockholm.
Justice minister Morgan Johansson
was spotted out shopping during the sales between Christmas and the New Year.
And finance minister Magdalena Andersson was photographed renting skies at a Swedish resort just before Christmas.
Mats Knutson, a political commentator for broadcaster SVT, observed that government ministers were perhaps grateful that the MSB’s outgoing chief had got himself into trouble.
“Now all the attention is instead directed at Dan Eliasson,” he wrote.