The six strong panel, headed by city council leader Gordon Matheson, were due to announce the winner at a ceremony in The Lighthouse tomorrow.
But that has been cancelled after the judges failed to agree on a winning design.
Because of other commitments, it will be next week before they can reconvene in the hope of agreeing which architect should be appointed to carry out the £15 million project.
Mr Matheson said: "It is disappointing but it is important we get this right. We will make a decision next week."
The other judges are David Mackay, partner with Barcelona based MBM Architects, Professor Andy McMillan, former head of the Mackintosh School of Architecture at Glasgow School of Art, David Harding, former head of environmental art at Glasgow School of Art and Geoff Ellis, boss of DF Concerts.
They have been considering plans for the square from four UK, one French and one American architectural firm.
Work on George Square is due to start within weeks, and one of the first jobs will be to take down the historic statues.
They will be removed for restoration but the decision on whether or not they are returned will depend on the final design for the area.
The cenotaph will remain in place during construction work.
Mr Matheson has said it is vital work on the square is finished in time for next summer's Commonwealth Games, when the city will be in the world spotlight.
The designs are on display in The Lighthouse in Mitchell Lane and can also bee seen at www.glasgow.gov.uk
The public can leave comments at the design centre or online until 5pm tomorrow.