Having beaten Ludogorets on away goals in the last round, the Israeli champions were drawn against the Slovenian's at Friday's draw.
Maribor beat FH Hafnarfjördur 2-0 on aggregate and have a good pedigree in the competition.
The first leg between Hapoel and Maribor will take place during the week commencing August 15, with the return leg the following week.
Maccabi begin their Ligat Ha'Al defence at home to Maccabi Netanya on August 19.
Maccabi Tel Aviv progressed to the playoff round of the Europa League after beating Panionios 2-0 on aggregate, but Bnei Yehuda were eliminated 2-1 by Zenit.