Owen Smith confirmed to Today that if his bid for a second referendum failed, he was likely to oppose the bill.
The SDLP's three MPs will also oppose the measure.
Ministers said MPs voting against Article 50 would effectively be trying to re-run the referendum in the hope of a "different answer".
"Parliament voted by a margin of six to one to put the decision on whether to remain in or leave the EU in the hands of the British people," said Brexit minister David Jones.
"Only the Conservatives can be trusted to respect the outcome of the referendum and make a success of Brexit."
Last week the High Court ruled Parliament must be consulted about leaving the European Union.
Unless the Supreme Court overturns the judgement in December, a bill to invoke Article 50 is expected in the new year.
Labour made clear its official position would be not to frustrate the process of leaving the EU after a newspaper report, external said the party leader Jeremy Corbyn intended to force a general election unless ministers caved in to demands.
After the story broke Labour sources said that while it would seek to amend the bill, it would provide "unconditional" support.
Shadow Brexit secretary Keir Starmer said Labour would not frustrate the process and would not vote down Article 50.
However, Labour and Liberal Democrat peers will try to amend the bill in the House of Lords. So too will one Conservative peer - Baroness Wheatcroft.