In its submission to a Scottish Government review of the board, the union said legislation introduced since its creation has rendered it no longer necessary - a point made by the NFU in England and Wales prior to the abolition of its board in 2013.
NFU Scotland policy manager Gemma Thomson said: "When the SAWB was established there was no National Minimum Wage, no Working Time Directive and no Gangmaster Licensing Authority. Nor were there the quality assurance schemes that check farm standards, including compliance with employment legislation. Other wages boards have been abolished and the SAWB should be too."
Thomson said a "serious competitive disadvantage ... is particularly keenly felt in the field vegetable and soft-fruit industries, which employ substantial numbers of seasonal workers and compete with farm businesses in England", pointing out that retailers "make no allowance for the extra costs imposed on Scottish businesses".
But Pat Rafferty, Scottish secretary at the Unite union, accused NFU Scotland of "advocating a race to the bottom on rural workers' rights".
"Reliance on minimums will mean pay cuts and freezes and longer working hours - this has been our experience of the abolition of the board in England."