The first major domestic showpiece of the English season was previously scheduled for February 28, 2021.
However, restrictions relating to the coronavirus pandemic in the United Kingdom have limited the attendance of fans this term.
Some stadiums are still allowed to house spectators, but their return in London was brief as the capital was placed under lockdown.
The EFL hopes a new Wembley Stadium date of 26 April, 2021 will enable supporters to make the trip.
"The number of fans permitted will be dependent on government guidance in place at the time and it is hoped that moving the date to later in the year will give clubs and their fans the best opportunity to attend in person." a statement read.
The competition is at the quarter-final stage, with last-eight ties to be played this week.
Holder Manchester City faces struggling Arsenal on Wednesday (AEDT) after Brentford host Newcastle United, with Tottenham at Stoke City and Manchester United travelling to Everton on Thursday.