The BMW International Open and the Open de France have been cancelled, while the the Scottish Open, due to be held in July, has been postponed.
The BMW International Open was due to take place in Munich from 25-28 June, but this year's event has been scrapped, as has the following week's Open de France because of the French government's decision to ban all mass public gatherings and events until mid-July.
However, discussions centring on the rescheduling of the Scottish Open are ongoing.
Keith Pelley, European Tour chief executive, said: "The decision to cancel the BMW International Open, which has been a cornerstone of the European Tour calendar for three decades, and the Open de France, one of our most historic national Opens was made in consultation with our long-term partner BMW and the French Golf Federation respectively, with public health and wellbeing the absolute priority for all of us.
"In consultation with Aberdeen Standard Investments, VisitScotland and Rolex, we have also decided to postpone the Aberdeen Standard Investments Scottish Open, which is part of our prestigious Rolex Series.
"Discussions about the possibility of rescheduling this event will continue as we look at a variety of different scenarios for our schedule for when it is safe and permitted to resume playing. We will only announce details of these plans when we have clarity on the global situation."
With 30 July - the slated start of the British Masters - the earliest possible return for the European Tour, Pelley is hopeful the current crisis will ease, allowing for no further interruptions.
"My primary message is actually one of optimism because I am genuinely hopeful that from now on the information I send in relation to our 2020 schedule will be positive," Pelley said.
"We cannot emphatically commit to a start date because, as I have said many times, we will not resume until it is safe, and we are permitted to do so.
"We now have 14 weeks with no tournaments, but those three and a half months are also the time where the global situation may well begin to show signs of improvement.
"There are already discussions centring around the easing of restrictions in several countries and everyone is optimistic that these can continue.
"This window also gives us the opportunity to continue working behind the scenes on a variety of scheduling options which would allow us to provide you with a busy calendar of golf to enjoy when we do resume."