Burnham, who took over as Britain's leader in July and said last month that Britain could consider rejoining the European Union in the future, is the first British prime minister to say openly there was evidence of Russian interference in the referendum a decade ago.
"I asked the question coming to Downing Street, was there interference in the 2016 referendum from Russia? And I've had the clear answer that yes, there was," Burnham said in an interview with The Rest Is Politics podcast released on Sunday.
Burnham did not spell out how he believed that Russia interfered in the referendum and gave no details on what evidence this statement was based.
The Russian embassy in London did not immediately respond to a request for comment.
Russia has previously denied meddling in the Brexit vote, casting Britain as gripped by anti-Russian hysteria.
Burnham's comments mark a departure from those of former Prime Minister Boris Johnson, who campaigned to leave the EU, and said in 2020 there was no evidence of Russian interference in the referendum.
Britons voted 52:48 per cent to leave the EU in 2016, plunging the country into its biggest political crisis since World War Two.
Burnham said voters in European democracies needed to be better informed about efforts to disrupt their politics.
"I mean, these things are important now to put clearly on the record, and I believe, help voters in Germany and France understand that some of this politics is instigated via our enemies, namely Russia," he said.
Britain's government failed to establish whether Russia meddled in the 2016 referendum on membership of the EU, according to a report by parliament's Intelligence and Security Committee in 2020.
The report also found that Russia had sought to influence Scotland's 2014 independence referendum, in which voters rejected independence.
Burnham last month said he could campaign to take Britain back into the EU at the next general election, reopening the country's divisive debate on its relationship with the continent.
