Arrest comes shortly after Cyprus detains ethnic-Azeri suspected of planning attack on military base for Iran.
Washington's support for Kyiv, already in doubt under President Trump, is set to decline further, analysts say.
NATO Secretary General Mark Rutte denied that the military alliance is acting hypocritically over the US strike on Iran.
Iran may close the vital maritime route, through which one-fifth of the world’s oil supply is shipped every day.