Jagoba Arrasate's men need to pick up all three points at the Donbass Arena to keep their qualification hopes alive, but their hosts are also desperate for a victory.
The Spanish side is bottom of Group A with two games remaining and it must secure all three points at the Donbass Arena and hope Manchester United beat Bayer Leverkusen to avoid crashing out of Europe's premier club competition.
Jagoba Arrasate's charges picked up their first point by holding the Red Devils to a 0-0 draw last time out and they will be out for revenge against the Ukrainian champions, who beat them 2-0 in San Sebastian back in September.
Sociedad comes into the game on a high after a thrilling 4-3 win against Celta Vigo at the weekend and it occupies fifth place in the Liga table.
Mexican striker Carlos Vela was the star of the show against Celta as he scored all four goals - including two in the space of three minutes late on - to seal a stunning victory.
Arrasate will be concerned by his side's form on its travels, however, as it has only won once on the road in the Spanish top flight this season to go with its 2-0 Champions League playoff win at Lyon in August.
In addition, midfielder Markel Bergara will not feature on Wednesday after picking up his third yellow card in the competition against United.
Shakhtar is two points behind second-placed Leverkusen and three adrift of leaders United ahead of the final two group games, with its last match at Old Trafford next month.
Mircea Lucescu's side has drawn its two home games in the group, but it will also come into the game on the back of an impressive victory, having beaten Sevastopol 4-0 at the weekend to cement top spot in the Ukrainian Premier League.
Shakhtar will be all but eliminated if it loses and the other game between Leverkusen and United at the BayArena is drawn.
Midfielder Bernard missed the resounding victory at the weekend as he had been away on international duty with Brazil, but he could return for this crunch clash.