The winners of Molde v Hibs enter the play-off round as the unseeded team, with a host of Europe’s big clubs lying in wait.
Braga, Feyenoord, Lech Poznan and Olympiacos were among the other potential draws for Neil Lennon’s side.
Zenit knocked Celtic out of last year’s competition, losing 1-0 in Glasgow but winning 3-0 in Russia to record a 3-1 aggregate victory over the Hoops.
They finished fifth in last year’s Russian Premier League behind the three Moscow clubs - Lokomotiv, CSKA and Spartak - and FC Krasnodar, but just seven points separated the top five teams.
The St Petersburg side had the joint meanest defence along with Lokomotiv, conceding just 21 goals over the season and scoring 46.
Among the club’s playing squad this year are Russian international duo Artem Dzyuba - who netted three goals at the World Cup - and Daler Kuzyaev, who played in all five of his Russia’s matches at the tournament; 105-cap Serbia international and former Chelsea defender Branislav Ivanovic and Robert Mak, capped 45 times by Slovakia.
Of their 102 Europa League matches (including games played under the UEFA Cup and Inter-Cities Fairs Cup banner), Zenit have won 54, lost 30 and drawn 18.
The Blue-White-Sky Blues won the Europa League in 2008, beating Rangers 2-0 in the final.
Since 2016 they’ve recorded wins over AZ Alkmaar, Maccabi Tel Aviv, Dundalk, Anderlecht, Bnei Yehuda Tel Aviv, Utrecht, Real Sociedad, Rosenborg and FK Vardar, as well as Celtic.
Dinamo Minsk finished second in the Belarusian Premier League last season, with BATE Borisov pipping them to the title on goal difference.
Like Zenit, they conceded the fewest goals over the course of the season, with just 15 goals scored against.
Former Hearts caretaker boss Eduard Malofeyev spent the bulk of his playing career with Minsk and has managed them on three separate occasions.
They have already seen off Derry City and Dunajska Streda in this year’s competition.
The play-off ties will be played on August 23 and 30.
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