The Security Service of Ukraine had detained the official, named in reports as Stanislav Yezhov, for acting “in the interests” of the “aggressor” after being recruited by Russian intelligence agencies.
Mr Yezhov accompanied Ukrainian PM Volodymyr Groysman on a visit to London in July and was photographed with his boss and Mrs May in Number 10.
Asked about the arrest during a press conference in Poland, Mrs May said: “I’m aware of the reports in relation to the Ukrainian individual who attended Downing Street earlier in the summer.
“The action that’s been taken is a matter for the Ukrainian authorities.”
Ukraine’s security service said Mr Yezhov acted “on the orders” of Russia to collect information “about the activities of government structures”, with the help of “special equipment”.
They allege he passed on data to the Russians through “electronic channels of communication”.
Mr Yezhov’s home and workplace are now being searched by Ukrainian security services.
The revelation came as Foreign Secretary Boris Johnson travelled to Moscow for a meeting with Russian counterpart Sergey Lavrov with relations Russia and the West sinking to Cold War levels.
Mrs May attacked Russia for “weaponising information” as she announced a UK-Poland defence treaty.
She said: “The Kremlin is seeking to undermine the international rules-based system, and it will not succeed.”
A Foreign Office spokeswoman said: “We are aware of reporting about the arrest of Stanislav Yezhov in Ukraine.
“We can neither confirm or deny the allegations against him. It is not our practice to comment on legal proceedings in other jurisdictions.”