The university previously concluded the ceremonies with a student leading a rendition after certificates had been handed out.
However, since last year graduates at the institution have not sung it.
God Save the King will now be played only when a representative of the Royal Family is present.
Current students told The Sun that the National Anthem provoked mixed reactions.
Layla Daynes, 21, added: “The monarchy isn’t really relevant to my generation, so it wouldn’t be missed.”
Annie Lawlor, 23, studying law, said: “It’s a bit old-fashioned to have it played at a ceremony supposed to be celebrating the achievements of the individual student.”
The move has been criticised by some, branding it “contemptuous”.
Free Speech Union director Toby Young said: “Why are Britain’s most prestigious universities openly contemptuous of the country’s history and heritage?”.
A University of Bristol spokesperson said: “The University routinely updates aspects of its Graduation ceremonies, which included the 2020 decision that the National Anthem would be played when representatives of the Royal Family, such as the Lord-Lieutenant, are in attendance.”
In November, the university announced it would distance itself further from slave trader Edward Colston following a public consultation.
Vice-chancellor and president of the university, Professor Evelyn Welch announced the decision to strip Colston’s emblem from the University’s logo.
In an open letter, she also apologised to those who had experienced racism at the institution.
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