The June 29-July 12 event will not be played behind closed doors and postponing the only Grand Slam grasscourt event until later in the year "is not without significant risk and difficulty", the AELTC said in a statement.
"The unprecedented challenge presented by the Covid-19 crisis continues to affect our way of life in ways that we could not have imagined, and our thoughts are with all those affected in the UK and around the world," chief executive Richard Lewis said.
"The single most important consideration is one of public health, and we are determined to act responsibly through the decisions we make.
"We are working hard to bring certainty to our plans for 2020 and have convened an emergency meeting of the main board for next week, at which a decision will be made."
Both the ATP and WTA tours are currently suspended until early June, effectively cancelling the clay-court season, and the French Open has been put back until late September, making the tennis circuit's traditional second slam the last of the year.
In addition to the postponement of the French Open, the 2020 Olympics have been put back to an as-yet-unannounced date, further disrupting the tennis calendar for the year.
The football European Championship, which was due to be held across several countries but with the final and both semi-finals in London, has already been postponed until 2021 due to the crisis, but that poses obvious logical difficulties due to its multi-host format.
Many figures from across tennis have made philanthropic donations to help deal with the crisis, with Roger Federer announcing a contribution of 1,000,000 Swiss francs to help his home country, which has been badly affected.