A Government spokesman said Tony Caplin - a former Conservative Party chief operating officer - had resigned as chairman of the Public Works Loans Board (PWLB) which is responsible for £60bn of loans in infrastructure projects.
It was reported Number 10 had been forced to act after an investigation it carried out revealed he had been made bankrupt in 2012.
Whitehall rules require anyone serving on a public body who is declared bankrupt to inform the responsible minister immediately.
A Government spokesman said: "Tony Caplin was appointed to a number of public bodies by the Labour Party. He was re-appointed to the PWLB by the Prime Minister.
"He should have declared he was bankrupt. This has been pointed out to him and as a result he has resigned."
Mr Caplin, who was at one time chairman of stockbrokers Panmure Gordon where Mr Cameron's father Ian was a partner, has also left his post on the Medical Research Council.
He has previously served on other public bodies including the North West London Hospitals NHS Trust, where he was chairman until January of last year.
He has been a commissioner on the PWLB for 10 years and in July 2013 he was appointed chairman by Mr Cameron.
He had been due to remain in the post until 2015.
Senior Labour MP Margaret Hodge, who chairs the Commons Public Accounts Committee, said: "This raises serious questions which should be investigated."
Shadow chief treasury secretary Chris Leslie called the situation "astonishing".
He added: "For him to be bankrupted in 2012 and appointed by the Prime Minister as chairman of this key Treasury body the following year is surely a misjudgement too far by a Prime Minister with a track record of poor judgment in relation to his cronies."