The paper reports that the Scottish virtuoso was "disgusted" at the university's announcement.
"This would not only restrict career choices in music," she said in a statement, "but also create an imbalanced university campus, and deny the local community the artistic benefits created by the university."
She added, "I would like to see some serious action from the government to help prioritize music as a just and valued subject on the curriculum at all levels, otherwise the future of arts education in th U.K. will become increasingly questionable."
The university plans to shut down or revamp all departments that are not internationally competitive, in order to get better research funding. Nine music-department jobs will be eliminated.
Glennie has been vocal on the subject of music education. She is a founding member of the Music Education Consortium and has been lobbying the U.K. government on the subject.
Glennie's is the second honorary degree returned to the university in the space of a week. Nobel Prize-winning scientist Harry Kroto sent his degree back as a protest against Exeter closing its chemistry department.
U.K. education secretary Charles Clarke, in response to Exeter's and other university's announcements about department closures, has asked the Higher Education Funding Council to look into what is happening to subjects of "national strategic importance," but his list of such subjects, which included science and language, did not include music.