Daniel Johnson, the Edinburgh Southern MSP who served as Justice Spokesperson, told Richard Leonard that he could not articulate his view that the UK should remain in the EU from the front bench.
Mr Johnson's resignation will come as a further blow to Mr Leonard, who earlier today saw campaign chief Neil Findlay quit the frontbench and announce plans to step down from Holyrood at the next election.
A long-time ally of the leadership, Mr Findlay called on the party to end infighting and a "toxic" culture of leaking and briefing.
Mr Leonard's party is still reeling from their abysmal result at last week's European Elections, which saw them fall from 2 MEPs in 2014 to zero, and slump to a vote share of just over nine per cent.
In his resignation letter, Mr Johnson, who was first elected in 2016, wrote: "I represent a constituency that voted 80% in favour of remain, where over 20,000 people signed the Revoke Article 50 petition and where the electorate voted overwhelmingly for parties that were clearly for remain and pro Europe.
"This election took Labour from first at the last European Election to sixth in Edinburgh. My constituents are clear not only that we must have another referendum but that we must make every effort to ensure the UK remains a member of the EU. This is a view that I share."
Before Daniel Johnson's resignation, and after a meeting of the party's MSPs at Holyrood, Mr Leonard insisted that he would not resign from the party he has led since November 2017.
Accepting that he was 'taking the flak' for the 'incredibly bad' result, Mr Leonard said: "Sometimes when your back's against the wall, people come together.
"We need to rebuild the Labour vote but we will do that by being united."
Two of the party's MP's, Ian Murray and Martin Whitfield, criticised both Mr Leonard and UK leader Jeremy Corbyn for their stance on Brexit, which they blamed for Labour's poor performance across the country.
Writing in the Scotsman yesterday, they described the result as a 'wake up call' for both Mr Cobryn and Mr Leonard.