The Armenian's safety was a concern because of the dispute between his country and Azerbaijan, the host nation of next week's fixture between the Gunners and Chelsea.
Despite receiving assurances aimed at allaying those fears, Mkhitaryan has chosen not to travel to Baku following discussions with the club and his family.
Arsenal boss Unai Emery said he respected the "personal" nature of Mkhitaryan's decision, but conceded it was "bad news" for his team.
But Arsenal managing director Vinai Venkatesham branded the situation "unacceptable" and revealed the club would make the full extent of their anger known to the governing body.
"I struggle to find words for how strongly I feel. We feel it's unacceptable," he said.
"We don't feel he can travel and it's extraordinarily sad. You don't get a chance to play in major European finals often. Miki has had it taken away from him and it is an extraordinary shame.
"We made our point clearly to Uefa, we have written to them. We will also sit down with them face to face after the final and express how it is unacceptable and how it can never happen again to Arsenal or anyone."
Mkhitaryan said he was "hurt" to miss the showpiece event.
He tweeted: "It's the kind of game that doesn't come along very often for us players and I must admit, it hurts me a lot to miss it."
Emery revealed he had discussed the issue with Mkhitaryan, whom he said "wants to play with the team but spoke with his family and decided not to go".
The Spaniard said: "It's bad news, but we cannot do anything about these issues. It's a very, very personal decision and we need to respect him. I don't understand the political problems, but I must respect (his decision).
"I spoke to him. I came from the Basque country, where we had a big political problem there, finishing five or six years ago. This is a very personal decision; I cannot push him to come with us.
"For him and for me, it's very important to (have his) help with his quality and his capacity, but these issues are out of my hands and I understand 100 per cent."
Uefa insisted that a "comprehensive security plan" was in place for Mkhitaryan, while the Association of Football Federations of Azerbaijan branded his decision not to play "unwarranted" and said the host country had "provided all the necessary guarantees" to ensure his safety.
An AFFA spokesperson said: "We very much regret this unwarranted decision taken, as we understand, collectively by Arsenal, the player and his family. Whilst we recognise the right to make a personal decision not to travel, we would like to reiterate that as the host country Azerbaijan has provided all the necessary guarantees required by Uefa to ensure the personal safety of Mr Mkhitaryan.
"There is no reason whatsoever to put in question the seriousness of these guarantees provided by Azerbaijan. Over the past decade a large number of Armenian athletes have taken part in various international sports events in Azerbaijan without any issues. Finally, we believe that this regretful decision will not affect in any manner the quality and the attraction of this great match. We look forward to welcoming both teams in Baku shortly."
Mkhitaryan's absence, in addition to that of the injured Aaron Ramsey, who is departing for Juventus, increases Mesut Ozil's hopes of starting at the Baku Olympic Stadium.
Like Ramsey, Petr Cech will not be at Arsenal next season, having taken the decision to retire at the age of 37, but Emery hinted that, despite losing his first-team place to Bernd Leno, the veteran goalkeeper is likely to start.
"Ozil has very big experience in Europe, playing with his national team, important games," he said. "We are preparing for every player to be ready for the final. He's working, he's trying, he's playing well and we need him.
"(Cech's) here because he deserves to be here. His commitment to Arsenal is big. He was playing the last (Europa League) matches, perfect matches, with big performances. I want to enjoy with him this final in his career."