Giroud joined Chelsea from Arsenal in January 2018, and will be hopeful of facing his former club in the Europa League final in Baku next week. Azerbaijan's Foreign Ministry reiterated that the Armenian player "can play" in Baku, dismissing fears over his safety.
Azerbaijan and Armenia are locked in a decades-long conflict over the disputed Nagorny Karabakh region.
UEFA later insisted that a "comprehensive security plan" was in place for Mkhitaryan.
"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", the player tweeted.
"Micki has been a key player in our run to the final", Arsenal said, "so this is a big loss for us from a team perspective".
Assurances had been offered by the United Kingdom ambassador of the Europa League final host nation, but not enough has been done to convince Arsenal and the player that he should make the trip to Baku.
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"We at all times put the sport as something very separate from these political issues and of course the same issue is again with Mkhitaryan", Azerbaijan Sports Minister Azad Rahimov said last week. Having failed to qualify for the Champions League next season through the Premier League, the Gunners have to win this one to make it to next season's competition.
Arsenal have already been critical of UFEA over the limited ticket allocation (6,000) provided to each club for the final, as well as the difficulty and cost of travel from London to Azerbaijan.
There are relatively few flights to Baku from Western Europe, though more are being operated for the final, and prices are far above usual levels.
A number of fans have since taken a stand against the decision to choose Baku's Olympic Stadium as next Wednesday's venue, demanding that the final be moved to a more suitable location.
While Arsenal will be without Mkhitaryan as they go in search of major silverware, Unai Emery is looking to claim a fourth Europa League success of his coaching career.
On Monday, the day before Arsenal's statement, Azerbaijan's ambassador to the UK, Tahir Taghizadeh, made attempts to ease Mkhitaryan's concerns over his impending decision to travel or not.