The BBC's decision to schedule the interview with Marr when the Prime Minister has still not committed to sitting down with Neil - who Jeremy Corbyn faced last week - has been branded "wrong" and "shameful".
It had been reported that the BBC had told Mr Johnson he would not be allowed to face Marr unless he also agreed to be interviewed by Neil too.
But in a statement, the corporation said: "As the national public service broadcaster, the BBC's first priority must be its audience.
"In the wake of a major terrorist incident, we believe it is now in the public interest that the Prime Minister should be interviewed on our flagship Sunday political programme.
"All parties' election policy proposals must - and will - face detailed scrutiny from us and we continue to urge Boris Johnson to take part in the prime-time Andrew Neil interview as other leaders have done."
Labour candidates have accused the BBC of "abject surrender" in allowing the Prime Minister to be interviewed by Marr without agreeing to an interview with Neil.
Ben Bradshaw, a former Labour culture secretary and candidate in Exeter, tweeted: "This is a shameful & abject surrender by the BBC management, which will leave professional BBC journalists absolutely horrified and in despair with an organisation where morale is already at rock bottom."
In a tweet, Ilford North candidate Wes Streeting said: "I love the BBC and hate the regular attacks on its impartiality and the professionalism of its journalists, particularly when it has some of the very best in the business. But this decision is wrong. The BBC have been played by the Tory Leader and shouldn't dance to his tune."
Mr Johnson has repeatedly refused to commit to an interview with Neil, despite other party leaders agreeing to be quizzed.
Mr Corbyn faced a brutal questioning from Neil on allegations of anti-Semitism within the Labour Party, in which he refused four times to apologise to the Jewish community.
Liberal Democrat leader Jo Swinson will be in the hot seat to face a televised half-hour grilling from Neil on Wednesday December 4, with Brexit Party leader Mr Farage taking his turn on Thursday December 5.
These follow the BBC's half-hour interviews with SNP leader Nicola Sturgeon and Mr Corbyn earlier this week, with three million people tuning in on Tuesday night to see the Labour leader face questions.
Meanwhile, the Conservatives and Labour have yet to confirm who will take part in an ITV seven-way debate on Sunday.
Mr Farage will be taking part in the podium debate, the first time he has during the 2019 campaign.
Ms Swinson, Ms Sturgeon, Greens co-leader Sian Berry and Plaid Cymru leader Adam Price are all confirmed to be taking part.
However, representatives for Labour and the Conservatives are still to be decided.
Mr Corbyn is scheduled to appear on Sky's Sophy Ridge On Sunday.
The parties took a step back from General Election campaigning following the London Bridge attack.
Mr Johnson and Home Secretary Priti Patel met with Metropolitan Police Commissioner Dame Cressida Dick and City of London Police Commissioner Ian Dyson at the scene on Saturday morning.