Mr Menzies was one of 287 sitting and former MPs to be named on a list issued by the Putin regime and is now banned from entering the country.
He said: “Along with 286 current and former parliamentarians, I have been made subject to sanctions by the Government of Russia and barred from entering the country.
“Those sanctioned have been identified by the Putin regime as the strongest in their support for the action taken in response to Russia’s unprovoked invasion of Ukraine.
“I have no issue with the people of Russia, the majority of whom are entirely innocent in these dreadful events.
“We cannot turn a blind eye to the horrors unfolding in Ukraine, in places like Mariupol and Bucha
“We are right to stand by the people of Ukraine in their time of needs and to stand up to Russian aggression.”
Blackpool North and Cleveleys Conservatives MP Paul Maynard is also on the list of those banned, as is Lytham-born Cabinet Office minister Stephen Barclay.
According to the Ministry of Foreign Affairs, the politicians listed "cannot visit the Russian Federation from now on".
A translation of a statement reported by state-owned Russian news agency RIA Novosti said the sanctions were being applied "on the basis of reciprocity", following the decision to sanction 386 members of the Duma after they backed Vladimir Putin's invasion of Ukraine.