The Scottish FA says it is “committed” to finishing the Scottish Cup and its preference is for the season as a whole to be completed.
The semi-finals, scheduled for 11 and 12 April, have been postponed, as has the final on 9 May.
Scotland’s European Championship play-off against Israel has already been delayed until June by Uefa.
Scottish football was suspended indefinitely on Friday due to the coronavirus crisis.
SFA chief executive Ian Maxwell says they “will consider future dates for the cup ties when the situation becomes clearer” but the decision to delay the cup final suggests the governing body does not expect any football to take place before May.
Maxwell added that it is “difficult to envisage” Scotland’s play-off with Israel taking place in June, despite Uefa’s announcement earlier on Tuesday, as European football’s governing body also delayed Euro 2020 by a year.
Hearts were due to face Hibernian and holders Celtic were to play Aberdeen in the last four of the Scottish Cup in just over three weeks’ time.
“It’s a flagship event for the Scottish FA and it means a lot to clubs, players, and supporters to watch their team lift the Scottish Cup,” Maxwell added.
“We want to give every supporter that can the chance to come and watch those games, so we’ll look to reschedule those games as soon as possible.”
The announcement from the Joint Response Group on the impact of the coronavirus, which has input from the SFA and the league body the SPFL, did not comment on when the Premiership and other domestic leagues might be able to resume.
It said only that group’s preference was for the season to be finished.
Hearts owner Ann Budge, whose side are currently four points adrift at the foot of the top-flight, says the club will consider legal action if they were to be relegated with the season incomplete.
Rangers managing director Stewart Robertson said on Monday the season must be finished to maintain the sporting integrity of the leagues.