The organisation has written to UEFA president Michel Platini asking him to use his influence to ensure that the governing body's "prestigious competitions are not tainted by such horrifying cruelty".
Shakhter killed the sheep before training for their home first leg tie against Celtic, which they went on to win 2-0 on Tuesday.
"The ritual slaughter of animals deeply upsets caring people worldwide and is already the subject of controversy," PETA's associate director Mimi Bekhechi said in the letter which was also forwarded to Reuters.
"May I please have your assurance that you will not permit the proposed killing of animals at stadiums that will host European football matches?"
The letter also points to UEFA's claims to be "forward-looking" and Platini's description of UEFA's "duty to protect the game, the players and our values".