Pyunik first qualified for European competition in 1996, after their second Armenian Premier League title earned them entry in to the 1996–97 UEFA Cup.
After a two-year break from European competition, Pyunik returned to the UEFA Champions League during the 2022–23 season.
Pyunik lost the first leg at home 1–0, but then went on to win 4–1 away in Luxembourg to secure a Third Qualifying round match up against Red Star Belgrade.
Pyunik were knocked out of the Champions League by Red Star in the Third Qualifying round, after being defeated 5–0 away in Serbia and 2–0 at home.
As a result of their defeat to Red Star Belgrade, Pyunik dropped down in to the UEFA Europa League, where they were drawn with Moldovan Champions Sheriff Tiraspol.