Chief executive Gordon Dewar said more than the previously announced 100 of its 750 staff were now facing redundancy - and the number could increase further.
He said the airport would remain open but large parts of the departure lounge will be in darkness and 12 of the 31 departure gates mothballed.
The south east and west piers will be closed, comprising gates one to four and 18 to 26.
One of the two immigration halls will also be closed.
Mr Dewar said flights had already been reduced by two thirds from the usual 340 daily and were “dropping by the day” because of the Covid-19 outbreak.
Car park bookings are down by 90 per cent.
Among the only flights to continue are likely to be aircraft bringing home passengers from abroad, and Royal Mail and medical shipments.
Mr Dewar said some UK flights were also still operating, but “how long that lasts remains to be seen”.
He said “lots of aircraft” had been laid up, but they would need to go on maintenance flights to keep them operational.
However, he said there had been a “modest” increase” in private flights, such as business jets.
Consultation over jobs
All but four of the 28 shops, cafes and bars in the terminal will close, with staff redeployed to high street branches where possible.
World Duty Free, Marks and Spencer, WHSmith and Wetherspoon are likely to be the only ones to stay open.
Mr Dewar said a six-week consultation with staff over jobs would start tomorrow until the start of May, which would include workers taking unpaid leave.
But he stressed: “It is very hard to put a final number on that, which depends on the number of voluntary redundancies and how long we have got this disruption.
“This is really a holding position.”
The airport chief said discussions were continuing over “payment holidays” and deferring “significant bills” such as business rates.
Mr Dewar said: “This is an unprecedented time not only for the aviation industry but for everyone as we all do what we can to ensure the health of ourselves and of those around us.
“For us, that includes the health of our airport.
“Our plan is based on keeping the airport open throughout and being there for those people who are still travelling and those staff members who are making that travel possible.
“We’re in a situation which is ever changing and as more countries enforce travel bans or special measures then it stands to reason that airlines will feel that impact and airports then feel that pain too.
‘Close to zero passenger demand’
“Unfortunately, that is happening now and we are trying to mitigate as best as we can and steer the airport through this situation in preparation for what comes next – and that is the biggest unknown in all of this.”
An airport spokesperson added: “Enforced travel bans across the world have resulted in airlines dramatically reducing their schedules to and from Scotland, directly impacting on passenger numbers at the airport.
“There was a small drop in passengers in February, with 935,455 passengers passing through the airport, which was 0.4 per cent behind February 2019.
“However, the airport is predicting a period of zero or close to zero passenger demand.”
Edinburgh West Liberal Democrat MP Christine Jardine said: “I appreciate the difficulties that Edinburgh Airport are facing. This is a time of crisis for them just as it is for everyone else.
“The fact they are remaining open for vital flights such as those transferring patients or delivering medical supplies will be of significant benefit to Edinburgh at this difficult time.
“I will be pressing the Chancellor for as much support for regional airports, which will have a massive role to play in driving forward local economies as we rebuild in the wake of this crisis.”
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