Beer Sheva will host the first leg against the Hungarian champions on July 11/12 with the second leg in Hungary the following week.
The match in Budapest will be played behind closed doors with the Hungarians being punished for racist chants the last time they appeared in European competition in 2013.
Beer Sheva, who were seeded in the strong half of the draw, will start as strong favourites, but manager Barak Bakhar cautions against over confidence.
"As we saw last season, there are no easy draws in the Champions League.
"We will study them, prepare as thoroughly as possible, and as always play to the best of our ability."
In the first qualifying round of the Europa League, Beitar Jerusalem will also meet Hungarian opposition in Vasas while Maccabi Tel Aviv play Albanian cup holders Tirana.
The matches will be played on June 29 and July 6.