The tournament was due to be played between 29 June and 12 July.
The entire grass-court season has been abandoned, and there will be no professional tennis anywhere in the world until at least 13 July.
Wimbledon is the latest major summer sporting event to be called off, with Euro 2020 and the Tokyo Olympics postponed for 12 months.
It follows the postponement of the French Open, which was due to begin in May but has been rescheduled to 20 September-4 October.
"This is a decision that we have not taken lightly, and we have done so with the highest regard for public health and the wellbeing of all those who come together to make Wimbledon happen," said Ian Hewitt, All England Lawn Tennis Club chairman.
"It has weighed heavily on our minds that the staging of the Championships has only been interrupted previously by World Wars but, following thorough and extensive consideration of all scenarios, we believe it is ultimately the right decision to cancel this year's Championships, and instead concentrate on how we can use the breadth of Wimbledon's resources to help those in our local communities and beyond.
"Our thoughts are with all those who have been and continue to be affected by these unprecedented times."