Chelsea will also have some travelling to do after they drew Belarus side BATE Boris, Hungarians Vidi and Greek side PAOK in Group L.
It would not be the first time Mkhitaryan has encountered this problem as he was left out of the Borussia Dortmund squad to play Gabala in Azerbaijan in 2015.
Azerbaijan and Armenia are in conflict over the Nagorno-Karabakh region and relations between the countries worsened in 2016 when at least 200 people were killed in clashes for which the Azerbaijan government has prohibited any Armenians from entering the country.
Arsenal will face Sporting Lisbon, Qarabag and Vorskla in Group E.
In a statement, an Arsenal spokesman said: "Safety and security of all our players and staff is always a top priority".
"Of course it hurts, but we will go on", added Rose, who remembered how he narrowly missed promotion as a player with German side Mainz 05 on several occasions.
Arsenal were one of four British clubs in Friday's group stage draw at the Grimaldi Forum in Monaco.
Leipzig and Salzburg were paired in Group B of Europe's second-string club competition alongside Scottish champions Celtic and Norwegian side Trondheim.
Whilst the attention has immediately turned back to the Old Firm game, Rangers' Europa League qualification has seen them drawn into a group alongside Villarreal, Spartak Moscow and Rapid Vienna in a fascinating group.
Steven Gerrard's Rangers are also facing a hard group stage, having been pitted against Villarreal, Rapid Vienna and Spartak Moscow in Group G.
It has been a long journey over the summer, as Rangers have seen off Macedonia's FK Shkupi, Osijek of Croatia, Slovenia's Maribor and then Ufa of Russian Federation in a surprise run under Gerrard.
The first round of group matches is on September 20.