Mr Gunnlaugsson, his wife and other Icelandic ministers were named in the Panama Papers. He had said no rules had been broken but was accused of concealing millions of dollars worth of family assets.
Icelandic readers have been sharing their views on the current political situation and how the protest may have played a part.
"I am shocked at how he chose to resign. He should have done that a long time ago. He didn't speak to his governmental department beforehand. The way he did it was entirely unacceptable.
"My gut feeling is that there is something very rotten in Iceland.
"Monday's protests were definitely something that Iceland has never seen before and the current situation is entirely unprecedented in Icelandic politics.
"I was inside looking out of the window and was startled by the egg thrown at the window, but the protest was 99% peaceful.
"I heard there could have been 22,000 at the protests. That would be 6% of the whole population - one of the largest protests we have had.
"It was a good atmosphere. I have never seen Iceland react in this way before.
"People are hurt and disappointed by Gunnlaugsson - it is not what they voted for.
"Even people who are loyal to the government are baffled - they have no words.
"One of the reasons why the government got a big following was that they said they'll take a strong hold of the economy.
"But the normal Icelander lost everything - their jobs, their homes, their future."
"I'm not surprised he has resigned. It was obvious this would happen eventually. I'm happy about it.
"He did the right thing but it should have been sooner. I hope they call for snap elections now. We won't stop protesting until we get that.
"The protests definitely put more pressure on Gunnlaugsson and everyone else in the coalition.
"It showed that we as a nation were not going to back down.
"There is definitely excitement and changes in the air here in Iceland."
"The prime minister, the finance minister, and the interior minister have all been named in the Panama Papers.
"I feel a mixture of anger, shame and betrayal - it's the same feeling I had during the financial crisis.
"Recently, Sigmundur Gunnlaugsson and the finance minister talked about the Icelandic Kronur being stable.
"But they keep their money elsewhere like they don't trust the system with their own money.
"In Iceland our welfare system is horrible - they are trying to privatise the hospitals and healthcare system because there's no money in the budget.
"If everyone paid their taxes we would have a good welfare system.
"The taxes go up on food but don't raise them for rich people.
"There's almost a divide in our country."
"Like half the nation, I've been watching TV live. It's been disrupting my work!
"Sigmundur Gunnlaugsson suggested his vice-chairman of the party would take over as PM. In my opinion that's not a good move.
"His resignation is like a scapegoat to allow the government to survive.
"It's obvious that the protests on Monday influenced this in one way or another.
"It's clear as day that this government has fallen and that we'll see a new election soon. It is purely based on the enormous reaction from the citizens of Iceland in the wake of the Panama television expose and his disregard to the public's reaction.
"On Monday you could not see a spot of grass at Austurvollur where the protests took place.  It was hard to wade through the crowds.
"Different kinds of people were there from the far left to the far right, from the old and the young - I was there with my children.
"The prime minister declined interviews with national TV for the last two weeks but he made an appearance elsewhere and said he hadn't thought of resigning, and that people wouldn't go out to protest in their numbers.
"Monday's protest was a blunt message to him. I was already planning to go to the protest but after Sunday's broadcast, I got really angry.
"I was flabbergasted after hearing about the Panama Papers, but it didn't surprise me. Both the prime minister and finance minister are businessmen so we could have guessed.
"They might not have done anything illegal but it was still wrong."
Comments compiled by Andree Massiah and Sherie Ryder
Sigmundur Gunnlaugsson has resigned as prime minister of Iceland after leaks from Panama law firm Mossack Fonseca showed he owned an offshore company with his wife.