Knopfler – former frontman of Dire Straits, whose hits include Money For Nothing, Brothers in Arms and Sultans of Swing – said Bearsden Primary "plays a vital part in community life".
East Dunbartonshire Council has infuriated parents and alarmed some local traders by proposing to shut the school and merge it with Castlehill Primary, a mile-and-a-half away.
Campaigners say the plan ignores Bearsden Primary's excellent record for educational attainment and its high school roll – which are both above the local authority average – and would force parents to ferry children by car instead of letting them walk.
Glasgow-born Knopfler, who attended the school for two years before moving to England in 1957, said: "I was dismayed to hear that Bearsden Primary is under threat of closure. I was very happy there.
"The school is ideally situated and I used to enjoy walking there and back every day.
"It sits in the heart of the catchment area – at Bearsden Cross – and there is no doubt it plays a vital part in community life."
Singer-songwriter Darius Campbell, famous for his appearances on Pop Idol and Pop Star to Opera Star, also sent campaigners a message of support on Twitter.
He wrote: "Please save Bearsden Primary School – it's the heart of the community. I can't imagine my childhood without it."
Wendy McLaren, a spokeswoman for the action group Save Bearsden Primary, said the high-profile support was a huge boost for the campaign.
Mrs McLaren, who has two children at the school, said: "This is not just about the proposed closure of a school. We believe shutting Bearsden Primary, which has been at the heart of our tight-knit community for more than 100 years, will have a negative impact on our whole community.
"We believe if the school is forced to move from its current location, it will have implications for local businesses and increased traffic congestion, and also stop our children from gaining the health and educational benefits of being able to walk to their local school in the heart of their community and catchment area."
The parents were dismayed to learn just two weeks ago that their school was being considered for closure under East Dunbartonshire Council's primary estate review.
On December 10, councillors voted 14 to 10 to go out to public consultation on a set of plans for school closures and mergers, which currently affects 24 out of the 36 East Dunbartonshire Council primaries.
Under Package A of the consultation, Bearsden Primary would be moved to, and merged with, Castlehill Primary. There is no option to retain and refurbish Bearsden Primary on its current site.
Package A also includes options for the merger of Westerton and Colquhoun Park primaries.
East Dunbartonshire Council said it needs to reduce the number of its primary schools because they "are operating at a level well below their capacity".
The council also claimed some of the school buildings "are relatively old and are not designed for the modern curriculum".
However, the move has also angered local businesses who fear they will lose their regular passing trade from parents and staff at Bearsden Primary, and led to concerns that long- established ties between the school and many community groups, including nurseries and clubs, and facilities such as the local library will be severed.
Some 10,000 surveys are to be distributed by the council to randomly selected households across the local authority area as part of a consultation on the plans. The surveys will be sent out from January 7 to February 4 next year.