According to The Courier, the MP for East Lothian was spotted at his constituency office in Dunbar on Monday, January 18.
Under current Scottish Government rules, which came into force on Boxing Day, 2020, people are only allowed to travel if it is “absolutely necessary”.
Scottish Lib Dems leader Willie Rennie criticised Mr MacAskill, saying: “As a former Justice Secretary, Kenny MacAskill must know that the law makers cannot afford to be the law breakers.
“He cannot sit in judgement of Dominic Cummings and expect to escape scot free when he copies his irresponsible behaviour.”
Martin Whitfield, Scottish Labour candidate for East Lothian in the upcoming elections, said: “On the day that Nicola Sturgeon has rightly questioned the need for Boris Johnson to make a trip to Scotland in the midst of a lockdown, we have learned that one of her own MPs is taking 400-mile round trips across the country.
“Having made huge sacrifices to stop the spread of the virus, people in East Lothian will be appalled to learn of their MP's apparent belief that the rules do not apply to him.
"Mr MacAskill rightly called for action against Dominic Cummings when his lockdown rules breach emerged, so it is only right that he should face the same scrutiny of his own actions."
Speaking at her daily briefing on Wednesday, First Minister Nicola Sturgeon said she had spoken to the party whip about Mr MacAskill’s conduct, but added that she did not know the full details of the incident.
The former Justice Secretary has admitted he had travelled the more than 200 miles to Dunbar twice, but insisted that both trips were for “medically-related appointments”.
A spokesperson for the 62-year-old said: “Mr MacAskill has a house in Moray, as well as a flat in his constituency.
“He returned north before lockdown to be with close family at Christmas.
“He has remained there during continued lockdown other than two visits for medical-related appointments.
“On one of those occasions, he attended his office to collect a set of keys stored there.”