Council leader Rhondda Geekie said the chamber had considered doing so, but had opted against the move.
The issue was raised after fellow administrations in Fife, West Dunbartonshire and Glasgow tendered their support for those civilians under siege in the Levant.
Mrs Geekie said: “We have considered this and have decided it is not a matter for the council and will therefore not be flying the Palestinian flag.”
On Friday, the Palestinian flag was raised above City Chambers on George Square, while Dumbarton Town Hall was first to fly the colours.
In last week’s Herald, the council said they would review the possibility of echoing the sentiments of their neighbouring authorities.
However, the idea provoked a strong reaction from many via social media.
Speaking on the Herald’s Facebook page, Andy Allan said: “There’s a Scottish and a UK government to deal with that stuff. If the local council can find time to bother with international issues then they’ve taken their eye off the ball.”
Dougie McNab added: “Try dealing with issues on our own doorstep before making any kind of political gesture regarding an issue which has little, if anything, to do with your electorate.”
There were also many who showed their support for the proposed move with Karen Watt posting: “Everyone should be appalled and stand up for the people of Gaza! All councils should do the same.”
Danny McFadden added: “The measure of any council, government or any official/authority group is the ability to rise above the normal day-to-day business and show support to extreme suffering somewhere else.”