The encounter with the Wasps was due to take place this weekend.
However, the Scottish Cup semi final clash with Hibs at Hampden Park resulted in the game being postponed.
The game at Tynecastle Park will now take place on Tuesday, November 24 with a 7pm kick-off.
Between now and the match taking place, Hearts will only be in action twice in the league, against Inverness CT and Dunfermline Athletic.
The match with Alloa will be the first between the two sides since Hearts’ previous season in the second tier. The Jam Tarts won all four matches between the teams that campaign, including a 4-1 victory at the Indodrill Stadium which included a fine Miguel Pallardo strike.
The last meeting at Tynecastle was a 3-0 win with Soufian El Hassnaoui amongst the scorers.
While Hearts have started with two wins from two, Peter Grant’s team have lost their first two.