The company, controlled by Rupert Murdoch, is in the middle of switching from analogue to digital broadcast technology and hopes to launch a version of the new service within three months.
Mr Carrington, who was aged 47, died on Friday night after a short illness. He had only been in the top financial position since the turn of the year.
He took over from Richard Brooke who left in November quickly followed by BSkyB's chief executive and managing director, Sam Chisholm, plus the deputy managing director, David Chance.
The official reason for the departures was that senior executives did not want the extra responsibility that would come from launching the latest phase of BSkyB development. But there were also reports of differences of opinion about the way forward.
More recently, there has been speculation that the BSkyB could lose Gerry Robinson, its chairman, because he holds the equivalent position at Granada, which has its own digital broadcasting interests.
Granada, which controls an 11 per cent stake in BSkyB, has been increasingly active with its partner, Carlton Communications, in British Digital Broadcasting.
Analysts said the latest upheaval at BSkyB comes at the worst possible time. Mr Carrington's death could create "a vacuum at the executive level", warned Paul Richards, media analyst with Panmure Gordon. "He [Mr Carrington] was a key member of the management team and no replacement comes to mind."
A BSkyB spokesman said it was too early to say who would replace the financial director, who was working a second stint at the pay-TV broadcaster.
He had been deputy director of finance from 1989 to 1991 but left to join Polygram before returning to BSkyB in 1995. Mark Booth, BSkyB's chief executive said Carrington's death was "a tragic loss". He said: "Nick had an incredible knowledge of BSkyB and was a strong presence during two key periods in the company's history. He will be missed very much by all of us."
BSkyB has traditionally built its support around sports programmes but increased competition has encouraged it to invest in made-for-television films.
It was a row between BSkyB and Carlton over the proposed acquisition of Premier football rights for digital channels that caused the conflict - and legal writs to fly - between the two.
Shares in BSkyB, which is 40 per cent owned by Mr Murdoch's News Corporation, rose 6.5p to 433p yesterday.Reuse content