Children from St Paul's Primary in Whiteinch were in tears when they realised their eco flag had also been stolen.
Head teacher Martin Hardie said: "The school is not usually hit by vandalism – we get the odd plant pulled out – so it was quite a shock to come in and see that."
"A girl from Primary 4 said two boys took it and it has gone to a bonfire somewhere.
"We have sent text messages to all the parents and all the children know about it, but we have not got any more information.
"It will be on a bonfire somewhere this weekend."
Mr Hardie said the flagpole would cost about £200 to replace.
An eco flag means a school has achieved a Green Flag status after taking part in initiatives designed to reduce, reuse and recycle items in their school day.
The St Paul's pupils earned their flag by taking part in activities such as tidying up the school grounds and picking up litter. They also recycle paper and monitor the school's gas and electricity use on a weekly basis.
Primary 5 pupil Tolu Giwa, 9, said: "That flag was important to the whole school. It is tragic that it has been stolen."
Underneath the green flag was also a Trinidadian flag in honour of the school's twinning with the island of Trinidad and Tobago.
Mr Hardie added: "We were just about to get a re-accreditation for the eco-award flag, which we won two years ago.
"We are more upset about that than the flagpole because it represents a lot of work the school had done.
"Both flags flew proudly in front of the school, making a statement about how eco-friendly we are and what we want to teach and also about our global partnership."
A police spokesman said "We are still looking into the theft, but there are no leads or no suspects. We are appealing for witnesses and asking anyone who may have seen anything to call Partick police office on 0141 532 3555."