Mark Thompson, the director general, ordered the cut after the BBC decided against selling off property assets, including Television Centre in White City, while the property market is in such a dire state.
Around 400 senior staff, including departmental heads, would have been entitled to a bonus of up to 10% of their salary if they met performance targets.
The bonus has been scrapped until further notice, while their pay will be frozen this year.
In addition, thousands of other BBC staff who would have expected a bonus this year were also told it will not be paid.
The freeze will save an estimated £20m while the rest of the BBC's 19,000 staff will receive a modest increase.
Thompson said: "A strategic contingency exercise, led by a senior group of managers, has been looking at what additional funds are needed should we need to put aside additional funds to cover our current estimate of the financial risks we face.
"It is important that we start this exercise now. We need to be in as strong a position as possible if we are to deliver distinctive content and meet our key strategic projects, such as moving to the new Broadcasting House, moving network production to the nations and funding our broadband future."
The move comes after a row erupted last year over the size of bonuses paid to BBC staff. It led to the BBC Trust, the corporation's governing body, demanding a freeze on bonuses for the executives in November.
Jana Bennett, the director of vision, saw her total pay including bonuses increase by 24% to £536,000 last year despite her being criticised in an internal report into the trailer for a documentary incorrectly suggested the Queen had stormed out of a photo-shoot.
It was also noted that Jenny Abramsky, the outgoing director of audio, earned a 27% bonus on her £419,000 salary, and left with a pension worth a hefty £190,000 a year.