More than 30 planes are being sent to bring back about 110,000 customers who are overseas - described as the UK's "biggest ever peacetime repatriation".
People were sent text messages at 04:00 BST telling them flights were cancelled - but some were already at airports.
Monarch employs about 2,100 people and reported a £291m loss last year.
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Passengers were then sent text messages informing them flights had been cancelled.
In all, the 300,000 cancellations could affect up to 750,000 people.
What have passengers said?
Mike Olley had been due to fly back to Birmingham from Malaga, in Spain, on Monday.
"We got a text this morning saying that Monarch had gone out of business,"
"I thought it was a prank. Our flight is at 12:15 back home today. We haven't got any information on our flight yet."
Katie Ode drove to Manchester Airport from Anglesey, north Wales, for a flight on Monday morning, but received a text message about Monarch when she was 10 minutes away.
the approach to the terminal was "chaotic", adding: "Stewards were stopping every car saying there was no point going into the airport."
He said they had already managed to book flights on another airline - costing a "fair bit of money", but he added: "I'm worried we've lost all the money on the flights. "
Advice to Monarch customers
Customers in the UK yet to travel: Don't go to the airport, the CAA says
Customers abroad: Everyone due to fly in the next fortnight will be brought back to the UK at no cost to them. There is no need to cut short a stay. Those with flight-only bookings after 16 October are unlikely to have Atol scheme protection, so will need to make their own arrangements
Customers currently overseas should check monarch.caa.co.uk for confirmation of their new flight details - which will be available a minimum of 48 hours in advance of their original departure time
All affected customers should keep checking monarch.caa.co.uk for more information
The CAA also has a 24-hour helpline: 0300 303 2800 from the UK and Ireland and +44 1753 330330 from overseas
What has gone wrong?
Monarch reported a loss of £291m for the year to October 2016, compared with a profit of £27m for the previous 12 months, after revenues slumped.
Blair Nimmo, from administrator KPMG, said its collapse was a result of "depressed prices" in the short-haul travel market, alongside increased fuel costs and handling charges as a result of a weak pound.
The transport secretary blamed a victim of a "price war in the Med".
However, Monarch chief executive Andrew Swaffield said the "root cause" was terrorism in Egypt and Tunisia, as well as the collapse of the market in Turkey.
He said it had been carrying 14% more passengers than last year - but for £100m less revenue.
Monarch's owner, Greybull Capital, had been trying to sell part or all of its short-haul operation so it could focus on more profitable long-haul routes, and said it was "very sorry" it had not been able to turn around its fortunes.
What have the authorities said?
The CAA said the situation was "unprecedented".
Chairwoman Dame Deirdre Hutton said there would inevitably be some disruption as the authority was having to effectively create one of the UK's largest airlines from scratch, adding: "It is a huge undertaking."
Passengers from as far away as Tel Aviv will require repatriation, and two "rescue flights" from Ibiza have already landed at Gatwick, the CAA said. The vast majority of customers due to fly on Monday are expected return by the end of the day.
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