The flag was flying to show support for the people of Ukraine who are under siege by Russian forces.
Councillor Buchanan said: “I put the flag up at the start of the conflict – like many other towns and cities across the world did – to show our support and solidarity with this courageous country and its people who are in a living nightmare.”
He said that he could not believe it when he realised that the flag had gone from the memorial gardens over the weekend and said the theft showed “a total lack of respect”.
He added: “I am just really disappointed – so many people saw the flag and said they were really pleased to see it flying there.”
Cllr Buchanan said that the flagpole had not been damaged and the ropes had not been cut when the flag was being removed.
“If someone had wanted a Ukranian flag all they had to do is contact me and I would have got them one. There was no need to take the community’s!” he said.
The Independent councillor, who was re-elected on May 5 to represent Bonnybridge and Larbert, pledged to get another flag put up in its place this week.
He said: “Hopefully those responsible will realise what they have done.”
Councillor Buchanan added that he has reported the theft to the police.
A Police Scotland spokesperson said: “We have received a report and enquiries are at an early stage.”