Shadow ministers Andy Slaughter, Ruth Cadbury and Catherine West were fired after defying the leadership to vote for an amendment calling to Britain to remain in the single market and the customs union.
A fourth frontbencher, shadow transport minister Daniel Zeichner, quit voluntarily after supporting the amendment.
In all, 49 Labour MPs voted for the amendment tabled by former shadow business secretary Chuka Umunna.
They included two other MPs, Rupa Huq and Gareth Thomas, who were still listed as being on the Labour front bench.
In the event the amendment was defeated by 322 votes to 101 with the rest of the Labour Party abstaining.
But with the SNP and Liberal Democrats backing the amendment, Mr Umunna said pro-European MPs from all parties would continue to fight against a "hard Brexit".
"While it is disappointing that our amendment did not win a majority of votes in the House of Commons, what it shows is that pro-European backbench MPs of all parties are not going to simply submit to a hard Brexit," he said.
"I and many others will continue to fight tirelessly to stop an extreme, destructive Tory hard Brexit.
"With a hung parliament, we have a real chance in future to shape Britain's exit from the EU to protect jobs and working people."
Tories said the vote showed Labour was in "total chaos" over Brexit.
Conservative MP James Cleverly MP said: "There is deep division at the heart of the Labour Party on the most crucial issue facing the country today.
"They still can't agree on the fundamentals and would get the worst Brexit deal at the highest price."
Liberal Democrat leader Tim Farron denounced Mr Corbyn for failing to back the amendment, saying voters would be left feeling betrayed.
"Millions of people who voted for Jeremy Corbyn were hoping for a new approach to Brexit," he said.
"They will be feeling utterly betrayed tonight that he has yet again failed to oppose this Government's extreme Brexit agenda.
"On the most important issue of the day, Jeremy Corbyn ordered his MPs to sit on their hands."