Standard Chartered has become the second corporate partner to sever ties with the Duke of York's business mentoring initiative Pitch@Palace.
The bank joined accountancy firm KPMG in pulling support for the scheme.
It said it was not renewing its sponsorship for "commercial reasons".
Several businesses and universities are reviewing their association with Prince Andrew following a BBC interview about his links to convicted sex offender Jeffrey Epstein.
Sources have told the BBC the decisions by Standard Chartered and KPMG were made before the interview.
'Very serious questions'
Meanwhile, Boris Johnson and Jeremy Corbyn were asked about whether Prince Andrew was "fit for purpose" during their head-to-head debate on ITV on Tuesday evening.
The Labour leader said there were "very, very serious questions that must be answered and nobody should be above the law".
The prime minister said: "I think all our sympathies should be, obviously, with the victims of Jeffrey Epstein and the law must certainly take its course."
In his Newsnight interview, broadcast on Sunday, the Queen's third child said he still did not regret his friendship with US financier Epstein - who took his own life in August while awaiting trial on sex-trafficking charges in the US.
The interview has provoked a backlash, with businesses, charities and other institutions announcing that they were reviewing their association with the prince.
In addition to Standard Chartered and KPMG ending their support for Pitch@Palace, pharmaceuticals company AstraZeneca and Hult International Business School are reviewing their partnerships with the business scheme.
Outward Bound, the charity the Duke of Edinburgh was patron of for 65 years, has called a board meeting to discuss the prince's patronage.
London Metropolitan University said it would consider the prince's role as its patron, saying it "opposes all forms of discrimination, abuse and human trafficking".
University of Huddersfield also students are calling for the prince to be sacked as their chancellor.
On Tuesday, the Huddersfield students' union panel passed a motion to lobby the prince to resign as their chancellor.
The university has since said that it listens to its students' views and will "now be consulting with them over the coming weeks".