Shadow ministers Yvonne Fovargue, Emma Lewell-Buckand Justin Madders, whip Stephanie Peacock and parliamentary private secretary Ruth Smeeth all resigned over the issue.
Labour's official policy is to keep the option of a second referendum on the table and Jeremy Corbyn's MPs had been ordered to abstain when the issue was pushed to a vote in the Commons.
But a total of 24 backed the call to delay Brexit in order to hold a second referendum, with 17 opposing it.
The shadow children and families minister Mrs Lewell-Buck defied the whip and resigned from her position last night.
Mrs Lewell-Buck's former boss, shadow education secretary Angela Rayner, said she had "made a principled stance and did what she believes is right by her constituents".
Sharing the post on Facebook last night, Mrs Lewell-Buck wrote: "I am so proud to have been in your team Angela we had some great wins for the most vulnerable.
"Thanks for everything, be cheering you all on from the back-benches."
Angela Rayner said: "Sad to hear the news that Emma Lewell Buck MP (South Shields) has resigned from our Shadow Education team.
"Emma was a superb Shadow Minister for Children and Families and worked so hard in her remit, her enormous contribution to protecting children and in particular the most vulnerable children was an area Emma felt very passionate about.
"Emma made a principled stance on her Brexit position and did what she believes is right by her constituents, l know Emma will continue to support our work as a backbench MP and work tirelessly for a Labour government. Much love and solidarity always."
Meanwhile, the Labour hierarchy - Mr Corbyn, shadow chancellor John McDonnell, chief whip Nick Brown and shadow Brexit secretary Sir Keir Starmer - held talks with two backbenchers who have put forward a plan to back Theresa May's Brexit deal in exchange for a referendum.
A Labour Party spokesman said they had a "useful and constructive discussion" with Peter Kyle and Phil Wilson "as part of Labour's engagement with MPs across Parliament to find a practical solution to break the Brexit deadlock".
The issue has deeply split Labour, with MPs representing Leave-voting areas unhappy with the prospect of being seen to betray their constituents while those in Remain-supporting areas have been under pressure to do more to oppose Brexit.