He said it was "very clear" his party accepted the referendum result.
Some shadow cabinet members are reportedly considering voting against triggering the UK's EU exit negotiations.
The Supreme Court will announce next Tuesday whether the government needs to seek Parliament's approval.
Ministers say they already have enough powers under the Royal Prerogative to go ahead with Brexit.
But campaigners argue that starting Brexit in this way would be undemocratic and unconstitutional.
In June's referendum, 51.9% of voters backed leaving the EU, while 48.1% supported remaining in the 28-nation group.
Mr Corbyn said: "It's very clear the referendum made a decision that Britain is to leave the European Union. It was not to destroy jobs and living standards or communities, but it was to leave the European Union and have a different relationship in the future.
"I have made it very clear that the Labour Party accepts and respects the decision of the British people. We will not block Article 50."
Asked if that meant he would be imposing a three-line whip - the strongest available sanction - on Labour MPs, requiring them to back Article 50, he said: "It means that all Labour MPs will be asked to vote in that direction next week or whenever the vote comes up."
The Guardian reports that four shadow cabinet ministers and several junior Labour spokespeople were considering defying Mr Corbyn and voting against Article 50 being invoked.
The Supreme Court's decision on whether a vote needs to take place follows a government appeal against a High Court ruling last autumn that MPs and peers should have to vote give their approval.
Following Mr Corbyn's comments, Green Party co-leader Caroline  Lucas said he was "trying to deny Labour MPs the chance to make their own principled choice on one of the most important decisions of the UK's recent history".
And Liberal Democrat leader Tim Farron said Mr Corbyn was "actively helping" the government in its plans to leave the European single market, "at a huge cost to jobs and prosperity".
Jeremy Corbyn says he will ask his MPs to vote for the Article 50 Brexit process to begin, if the government is forced to seek Parliament's approval.