Ben Bradshaw said Moscow’s likely interference in the vote would fit a pattern of meddling in other nations’ affairs, following the CIA’s accusation that Russian hackers tried to influence the recent US elections.
He said: "I don’t think we have even begun to wake up to what Russia is doing when it comes to cyber warfare.
"Not only their interference, now proven, in the American presidential campaign, [but] probably in our referendum last year. We don’t have the evidence for that yet. But I think it’s highly probable."
Last week the CIA claimed that Russia had interfered with the US election and actively helped Donald Trump win the White House.
The agency suggested emails hacked from the Democratic Party and given to the WikiLeaks website aided the Republican candidate’s win in November’s race.
Mr Bradshaw also pointed to French elections where Marine Le Pen’s National Front asked Russia for a £23m loan to help it fight presidential and parliamentary campaigns in 2017.
German politicians and intelligence officers have warned that hackers and others acting for the Russian state could undermine Germany's general elections next year.
Mr Bradshaw went on: "When will we realise that Russia’s strategy is to weaken and divide the free world and that driving the biggest refugee flows into Europe since World War Two is a deliberate, a deliberate, part of that plan.
"When will we admit that what Putin can’t achieve militarily he is already achieving using cyber and propaganda warfare."
A Downing Street spokesman said he had not seen any evidence of Russian interference in the EU referendum.
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