The Ivorian defender was dismissed after putting a hand to John Guidetti's face, with Facundo Roncaglia then also seeing red for retaliating in the aftermath.
United were not punished, however, with Guidetti missing a late chance to send Celta into the final at the home side's expense and United triumphing 2-1 on aggregate after a 1-1 draw at Old Trafford.
2 - Eric Bailly has now been sent off twice in the Europa League in 2016/17, more than any other player in the competition. Mist.— OptaJoe (@OptaJoe) May 11, 2017
Ajax - a team filled with youth - lost 3-1 on the night but progressed 5-4 on aggregate after a 4-1 victory in the first leg.
Mourinho will bemoan the loss of Bailly for that match, however, with the new signing from Villarreal having quickly established himself as United's first-choice centre-back.
The Red Devils are currently without Timothy Fosu-Mensah, Marcos Rojo and Luke Shaw in defence, but have Chris Smalling and Phil Jones back in contention after injuries.
Smalling appeared as a late substitute after Bailly's red card and may have landed himself a starting berth in Stockholm as a result of the suspension, with Daley Blind and Jones the other available options.
United have also lost Zlatan Ibrahimovic to a season-ending injury but were carried through to the final by 19-year-old Marcus Rashford, who scored their only goal in the away leg and produced a superb assist for Marouane Fellaini's opener on Thursday night.
Roncaglia equalised a couple of minutes before he was sent off but United held on to reach the Europa League final for the first time in their history.