He was also present at a meeting with then US Vice President Joe Biden at the White House in 2016.
Mr Yezhov was detained by Ukraine’s SBU security service in Kiev on Wednesday. Footage showed him being led away by two officers.
Asked about the issue during a visit to Poland, Ms May said she was aware of the reports of Mr Yezhov’s arrest but that it was a matter for Ukraine.
She 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.”
Ukrainian security services claimed Mr Yezhov had acted “on the orders” of Russian intelligence agencies and had used “special equipment” to collect information “about the activities of government structures”.
The information was passed to Moscow via “electronic channels of communication”, they said.
Mr Yezhov’s home and workplace are now being searched by Ukrainian authorities. He will probably face charges of treason, officials said.
Mr Groysman said on his Facebook page that the suspect had worked “for a long time in the interests of a hostile state”.
The issue could be raised when Boris Johnson, the Foreign Secretary, meets his Russian counterpart, Sergey Lavrov, in Moscow on Friday.
The revelation came as Ms May used her trip to Poland to accuse Russia of “weaponising information” as she announced a UK-Poland defence treaty.
“The Kremlin is seeking to undermine the international rules-based system, and it will not succeed,” she said.
A Foreign Office spokesperson 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.”
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