UCU Scotland, the union that represents lecturers, said the suggestion was "xenophobic" and failed to take account of the global reach of modern universities.
The attack came after Alfred Baird, professor of maritime business at Edinburgh Napier University, said Scottish academics were a "rapidly diminishing species" as universities recruit staff from across the world.
Mary Senior, the UCU's Scottish official, said: "We should be proud that Scottish universities can attract the brightest and best from the rest of the UK and from across the world to live, work and learn in Scotland.
"To suggest that our universities are being 'swamped' is xenophobic to say the least, and fails to understand the fast- moving, interdependent world that we live in today, where global connections can benefit us all."
Writing in the online magazine Scottish Review, Mr Baird said Scots academics were fast becoming a minority in many teaching departments and research centres in Scotland.
A spokeswoman for Universities Scotland, which represents university principals, has already dismissed the concerns.
"All our universities compete and succeed on a global stage," she said.
"The international mobility of academic staff and ideas is a key ingredient of this success."