He was Groysman's interpreter during his time as speaker of the Verkhovna Rada and later followed him to the Cabinet of Ministers when he became prime minister in 2016.
Ukraine and Russia were once allies whose intelligence agencies often worked closely together, but relations deteriorated after Russia's annexation of Crimea in 2014 and support for pro-Russian separatists in eastern Ukraine.
Stanislav Yezhov, who accompanied the country's prime minister on numerous trips, was detained in Kiev on Wednesday. "I'd like not to talk about this anymore", she said in response to journalists' request to comment on the actions of Ukraine's Security Council and the Ukrainian mass media reports on the situation.
Ukraine's Prime Minister Volodymyr Groysman posted about the arrest on his Facebook page.
'He was respected. And he responsibly and diligently worked for the Russian special services'.
In June 2016 he visited the White House and interpreted for Groysman during a meeting with the then United States vice-president, Joe Biden.
They said Mr Yezhov, who is facing charges of treason, used "special equipment" to gather information which he then passed on to his Russian handlers. "The intruder transferred the collected data via electronic communication channels", the press office of the Security Council reported.
The SBU did not directly refer to Mr Yezhov but he was named by other senior officials.
A spokesman said: "We've read news but we have no information".
The SBU said in a statement that the official was recruited by Russian agents while he travelled overseas.
She said: "The Kremlin is seeking to undermine the worldwide rules-based system, and it will not succeed".
"We can neither confirm or deny the allegations against him".