The Royal Blues appealed the decision by Scottish referee Craig Thomson to dismiss Matip for denying a clear goalscoring opportunity when he brought down Luuk de Jong.
Thomson also awarded Twente a penalty in the incident, which De Jong scored as the Dutch side won 1-0.
UEFA rejected Schalke's appeal, claiming there had been contact, albeit slight, between the two players, which meant the referee's decision could not be rescinded.
But the German club have lodged a further appeal against the decision, meaning Matip's suspension will not come into force until the governing body's disciplinary committee issues its ruling.
The committee are not going to now discuss the issue until Friday, so Matip is available to face Twente at the Arena AufSchalke.
"This is the right decision and of course it is good news for us," Schalke's director of sport Horst Heldt said.
"I think that this is fair since we were already placed at a disadvantage due to an incorrect decision in the first leg. At least for the time being, we have not been punished twice.
"First and foremost, it is important that Joel is available against FC Twente since we are short of options in defence."
In the first leg, Matip was sent off despite De Jong appearing to clip his own heels, with the striker also going down outside the area.
Coach Huub Stevens called on the team to forget that match, though, and focus on overturning the deficit.
"But we must not dwell on the first leg anymore - that is now behind us and we can no longer influence it," he said.
"We know that Twente are in the better situation, but our aim has got to be to strike at the right moment."
Stevens is particularly happy to have the competition's second highest goalscorer Klaas Jan Huntelaar available after he missed the first leg.
"It's important that Klaas Jan is back on board again because he has special qualities," he said.
Twente coach Steve McClaren is preparing to return to Germany for the first time since being sacked as Wolfsburg boss just over a year ago.
His side go into the game on the back of a 3-1 Eredivisie defeat to NEC Nijmegen, which hit their chances of winning the title.
The defeat left them four points off leaders AZ Alkmaar, although they have a game in hand.
"I have said since I arrived here that we are just one of six clubs in with a chance of winning the league and that has not changed after losing to NEC," McClaren told Voetbal International magazine.