The decision to postpone the tour, taken by the Cricket West Indies, came as a result of the uncertainty for the safe resumption of cricket in the United Kingdom, as well as international air travel.
Chief Executive Officer of CWI, Johnny Grave said: "Clearly playing in June is now not possible and we will continue our discussions with the ECB and other internationals boards on trying to find new dates."
"We will only travel to England to play the series if our players can be assured that it is safe to do so. Our respective medical teams are beginning to discuss how this series could be played whist guaranteeing the health and safety of our players and support team. We will be as flexible as we can without compromising the safety of our team," he added.
The England and Wales Cricket Board (ECB) has already announced that no professional cricket will be played in England and Wales until at least July 1 due to the Covid-19 pandemic.
An ECB Board meeting on Thursday approved a number of measures which would significantly restructure the English season if some cricket is played this summer.