The heads of both institutions have written to Chancellor George Osborne to express concerns that the change could undermine their fundraising efforts, The Times reports.
Andrew Hamilton, vice-chancellor of the University of Oxford, argues that the cap “risks undermining the culture” of philanthropy in the sector.
Leszek Borysiewicz, vice-chancellor of the University of Cambridge, writes that the implications of the change “will be significant”.
The proposals, announced in the Budget on 21 March, would cap the amount of tax relief donors can receive at £50,000 or 25 per cent of their income, whichever is higher.
The changes could reduce large donations because donors would not be able to recoup as much of their gifts in tax.
Vince Cable, the business secretary, has said he is concerned about the impact the plans could have on the academy.
Universities UK and the Russell Group of large research-intensive institutions have also voiced their fears that the rules could hit donations.
In 2010-11, the sector received £560 million from philanthropic sources, accounting for just over 2 per cent of its income.
Oxford and Cambridge received 44 per cent of all new donations pledged, according to the Ross-Case survey of university philanthropy.
The rest of the Russell Group garnered 26 per cent, while the 1994 Group of smaller research-intensive institutions received 9 per cent.