Jeremy Hunt said he was “extremely worried” about the former US Marine, who has been detained on suspicion of spying.
He added that “every support” is being given to the 48-year-old.
Mr Whelan’s family said he was attending a wedding, while Russia said he was “caught spying” in Moscow.
Mr Whelan was born in Canada to British parents and moved to the US as a child. He now lives in Michigan and is director of global security for automotive components supplier BorgWarner.