The club wanted the match to be called off due to a virus outbreak among members of the squad.
Given that only a limited number of players are fit and healthy for the game, the governing body has opted to push the fixture back to Tuesday, April 12.
A statement from Hearts read: "Heart of Midlothian FC applied to the SPFL earlier today for the postponement in view of injuries and/or sickness affecting the vast majority of the first-team squad, which has left the club with few fit players including only one fit goalkeeper over the age of 16.
"The Heart of Midlothian FC doctor has provided written evidence to the SPFL of the injuries and sickness of all those affected and has also advised of the potential for further infection, both of other squad members and of players and staff of Inverness Caledonian Thistle FC.
"In these exceptional circumstances, the SPFL has agreed to the postponement request."
Hearts are currently third in the Scottish Premiership table.