Sinn Fein has called for a border poll on a united Ireland following the UK's vote to leave the EU.
Northern Ireland voted to remain in the EU in Thursday's poll.
Results showed that 440,707 (56%) people voted to Remain and 349,442 (44%) voted to Leave. Of the 18 constituencies, 11 voted Remain and seven voted Leave.
Sinn Fein backed the Remain campaign.
Speaking to RTE, Mr McGuinness said the British government has a "democratic imperative" to call a referendum on whether Northern Ireland should leave the United Kingdom and unite with the Irish Republic.
He added: "The British government now has no democratic mandate to represent the views of the North in any future negotiations with the European Union and I do believe that there is a democratic imperative for a border poll to be held.
"We are now in unchartered waters, nobody really knows what is going to happen. The implications for all of us on the island of Ireland are absolutely massive. This could have very profound implications for our economy."
The party's national chairman Declan Kearney said the question of Northern Ireland remaining as part of the UK had now been brought into sharp focus.
"We have a situation where the north is going to be dragged out on the tails of a vote in England," he said.
"That is a huge democratic deficit for our society, building on the existing democratic deficit of partition.
"The British Government have now forfeited its mandate to represent the north of Ireland in relation to the European Union."
He added: "We now have a situation where Brexit has become a further cost of partition, a further cost of the Union and Sinn Fein will now press our demand, our long standing demand, for a border poll."
A border poll can only be called by the region's Secretary of State in circumstances where there is clear evidence of a public opinion swing towards Irish unity.
UUP leader Mike Nesbitt criticised Sinn Fein for "adding further uncertainty".