Australia's national carrier grounded its global fleet indefinitely until unions representing pilots and ground staff reach an agreement with the airline over pay and conditions.
The dispute will affect 70,000 passengers worldwide and 600 flights on one of the country's biggest travel weekends, Qantas said.
Among those hit are 17 Commonwealth leaders who, after attending a summit hosted by Australia's prime minister Julia Gillard, have been left stranded in Perth.
Ms Gillard said that the dispute could have implications for Australia's economy.
"The Qantas dispute escalated today and I am concerned about that for the national economy ... it could have implications for our national economy," she said.
The airline has been hit by a series of strikes since the company's management announced a restructuring and outsourcing plan in August.
The union members have expressed concerns about the proposal, saying it would result in job cuts in Australia.
A Heathrow spokesman said four Qantas liveried planes were due to take off from the airport today - meaning hundreds of passengers who were scheduled to depart are now unable to fly.
British passengers abroad who are due to use the carrier will also face travel disruption.
The Foreign Office issued a statement advising those due to travel with the airline in the next 48 hours to check on the Qantas website or to consult their tour operator.
The carrier plans to "lock out" all employees involved with industrial action from Monday evening. Staff will not be required to turn up at work and will not be paid.
The airline had been forced to reduce and reschedule flights for weeks because of a series of strikes over staff concerns that their jobs are being moved overseas.
Flights already in the air when the announcement was made were continuing to their destinations but all others were cancelled.
The airline said customers booked on Qantas flights should not go to the airport until further notice and a full refund would be available for those affected.
A spokesman said: "Qantas regrets that this action has become necessary and apologises sincerely to all affected passengers."
A spokeswoman for British Airways, which has a joint services agreement with the airline, said: "British Airways-operated flights between the UK and Australia are not expected to be disrupted at this time.
"Customers who are booked to travel on a British Airways service operated by Qantas are urged to check the status of their flight.
"If your travel commences within the next 24 hours please contact our call centres to discuss alternatives."