Income from investments has dropped sharply and the FTSE 100 index of leading companies recently hit a five-year low.
Eton College has already told parents it will have to put fees up by more than the inflation rate, and other elite institutions are expected to follow.
Mike Sant, of the Independent Schools Bursars Association, said: "Schools that use income from endowed funds may find scholarship funds have been depleted. The choice is to make up the money by other means or cut the number of scholarships."
Schools with endowed funds are mainly large institutions such as Eton, Winchester and Harrow, he said.
John Shuffrey of Saffery Champness, the specialist accounting firm said schools would have difficulty reducing scholarships. "Once they are offered, you have got to maintain them."
With a government review of private schools' charitable status under way, "the last thing most schools want to do is to be seen as reducing bursaries", he added.
Steven Little, chief accountant at Winchester College, said an emerging recession could mean a growth in demand for bursaries and scholarships.
Plummeting stock markets could also hit local authority spending on education. Experts say that because pension funds will see their value fall, authorities may have to increase employers' contributions. This could mean less money for other services.
And it could affect other parts of the education service. Shares in business support services company Amey, the pound;2 million sponsor of Unity city academy in Middlesbrough, were this week trading at a four-year low.
The company is involved in the biggest education public-private partnership deal, a pound;1.2 billion upgrade of schools in Glasgow.
It is also working with Nord Anglia to improve education services in Waltham Forest, a north-east London borough severely criticised by the Office for Standards in Education. WS Atkins, which runs some local education services in Southwark, saw its shares fall 6 per cent this week, while Serco, the firm working with Bradford LEA, fell 13 per cent. Also affected are Jarvis, builders of the first private finance initiative school, Colfox in Bridport, Devon. Its shares dropped 5 per cent.