Nicola Sturgeon announced on Friday all non-essential travel to Manchester and Salford would be banned from Monday, but the Labour mayor said neither he or his administration were contacted before the announcement.
The First Minister pinpointed the areas as Covid-19 hotspots, despite figures in the cities matching case rates in parts of Scotland.
“Anyone travelling elsewhere in the Greater Manchester or Lancashire area, I’d ask to think carefully about whether your journey is really necessary, because we do see cases rising across that region,” she said on Friday in a coronavirus briefing.
Speaking on The Andrew Marr Show on Sunday, Mr Burnham said: “I was really disappointed on Friday that the First Minister of Scotland just announced out of the blue, as far as we were concerned, a travel ban saying that people couldn’t travel from Scotland to Manchester and Salford and people couldn’t go the other way.
“That is exactly what the SNP always accuse the Westminster Government of doing, riding roughshod over people.
“The SNP are treating the north of England with the same contempt in bringing that in without any consultation with us.”
He added: “I just think it’s double standards, it’s hypocrisy.
“They’ve done to us exactly what they always complain that the UK Government does to Scotland.”
Mr Burnham said he would be looking for his constituents who planned to travel north of the border to be financially compensated by the Scottish Government.
“I’ll be writing to the First Minister today,” he said.
“I’ll be asking for compensation for the individuals who might lose holidays and the businesses who might lose bookings.
“Why should a couple from Salford who are double jabbed who are about to go on a walking holiday in Scotland not be able to go?
“It’s completely disproportionate in my view – we could have come up with a different arrangement if the First Minister had been in touch with us.”
Mr Burnham went on to say there should be “an arrangement” put in place, which would mean there would have to be consultation between Scotland and the north of England before such a travel ban was put in place.
The Manchester mayor’s comments come as Scotland recorded 1,205 cases of coronavirus in the past 24 hours, with no registered deaths.
The positivity rate also remained high compared with recent months, rising to 5.8% of all tests, compared to 4.5% the day before.
The NHS Lothian health board area saw the highest number of new cases, with 321, followed by Greater Glasgow and Clyde on 294 and Lanarkshire on 125.
Scottish Government trade minister Ivan McKee said a decision on Covid-19 had to be made quickly.
“The virus, as we know, moves very fast, decisions are made very fast and those decisions are communicated at a four nations level,” he said.
“Andy Burnham… is going to write to the First Minister about it, that’s absolutely fine and I’m sure there will be a conversation about how we can keep him better informed in future.”
But Tory leader Douglas Ross, speaking on the same show, said: “We know that law was made on Thursday morning to introduce these restrictions into Greater Manchester and a ban on travel, yet it wasn’t announced until over 24 hours later.
“If Ivan McKee says there’s not good enough dialogue between the UK Government and the Scottish Government, there was 24 hours that passed before anyone in Greater Manchester knew of a decision taken by the Scottish Government a day earlier.”