The scientists have objected to the Royal Society's use of a ballot paper that only allow them to vote "yes", 'The Sunday Times' reported.
The report said the Duke of York was elected with just 11 per cent of the vote, following a huge number of abstentions.
The objectors have told Sir Paul Nurse, the society's President, that they oppose the choice of Andrew and the way the election was conducted.
While Lord May supported the society's association with royalty, others want the links to be reduced.
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"My immediate reaction when I heard the Royal Society council had ratified this was shock," said Peter Lawrence, professor of molecular biology at Cambridge University.
"The indiscriminate election of royal fellows, and it seems to me this case offers strong evidence of lack of discrimination, can only harm the reputation of the Royal Society," he added.
He told Sir Nurse that he was opposed not only to the prince's election but to the whole system of electing royalty as fellows.
"The Royal Society was founded to advocate the idea that science is what matters, not deference to authority. The exception to that seems to be deference to 'royal blood', but it is taking deference too far to elect Prince Andrew," he said.
In a blog, Colquhoun pointed to a series of controversies involving the Duke including the sale of Sunninghill Park, his former home, to Timur Kulibayev, the son-in-law of the Kazakh president. The property was sold for 15 million pounds, at least 3 million pounds above the asking price.
Sir Nurse accepted the voting system was "an anachronism" which had to be changed. "We have had many other votes conducted like this but it needs to be brought up to date," he said.
Andrew's election gives him a place alongside scientific luminaries such as Stephen Hawking, Sir Tim Berners-Lee, the inventor of the world wide web, and Sir John Sulston, who oversaw the human genome project.