Stevenson looked set to miss the Easter Road clash with Inverness on February 2 after incurring a two-match ban following his red card for clashing with St Johnstone goalkeeper Alan Mannus during Saturday's 3-3 draw at McDiarmid Park.
But the Scottish Professional Football League has announced that St Mirren's visit to Tynecastle, which was originally scheduled for February 1, will now take place next Wednesday.
Hearts suggested the new date and St Mirren agreed, meaning Stevenson will miss this weekend's game against Ross County and the Buddies clash.
Manager Gary Locke told Hearts TV: "That was one of the reasons why we tried to get the game organised.
"I think you saw in the games this season where Ryan has been missing he has been a big loss to the team.
"Obviously the semi-final is a huge game and we'll give ourselves a better chance by having all our best players on the pitch.
"So I'm delighted St Mirren have kindly agreed to rearrange that fixture. It's not ideal in as much that we have a game five days before the semi-final but it's great we have got Ryan available for such a big game."
The news is the second boost for Hearts since Sunday, when administrator Bryan Jackson announced that assistant manager Billy Brown would be able to continue in his role until the end of his contract.
It had previously been announced that the St Johnstone game would be the last match of Brown's third spell at Tynecastle but he will now keep working until January 31, and he is expected to be beside Locke during the semi-final two days later.
Goalkeeper Jamie MacDonald was among the players that Jackson consulted over the decision and he welcomed the news.
MacDonald told Press Association Sport: "It's a massive boost for everybody at the club because the last thing we were wanting with two weeks to go before the cup semi-final was upheaval.
"You just want to have a bit of continuity going into the game and that would have upset things a bit because we have a good working relationship with the gaffer and Billy and (goalkeeping coach) Alan Combe and the boys.
"It was the administrators who came to us and wanted to get our views on the situation, which is fair play to them. They have taken our advice on board.
"It's a very difficult season and it's stressful for everyone. I think from the gaffer's point of view, Billy takes some of the stress away, even by doing media commitments sometimes.
"And for the players, Billy is very involved in training and one thing we have got is a great team spirit and Billy is probably a large part of that. He likes to have a laugh and a joke at times in training and keeps the boys geed up so he is a big influence on everybody."
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