Interserve was due to start the job this month.
But construction has been put on hold while the project is value engineered in a bid to keep costs down.
A statement from the National Galleries of Scotland said: “Work on the construction of new Galleries was due to start in March.
“However, there will now be a delay of several months to the full start on site.
“For the past six months we have been working with our main contractor Interserve on the detailed designs and various tender packages for the building work.
“It has become clear that some elements around the delivery of the construction work are more complex and potentially more expensive to implement than was originally anticipated.
“We therefore have to carry out some value engineering in the coming months in order to streamline some parts of the construction and bring the plans into line with our budget.
“In practice this means that we will be re-examining some of the specifications and construction methods for aspects of the design to ensure that the project stays within cost.
“Until this work on value engineering is complete we will not have a confirmed date for the start of construction but we are hopeful that we can begin work on site later this year.”