A Transport Scotland spokesman said a small number of workers downed tools on Wednesday and that AWPR CJV joint venture main contractors Balfour Beatty and Galliford Try were seeking to resolve issues.
A spokesman said: “We are aware that a small number of operatives downed tools in dispute with their employer and the CJV is holding discussions with Rossmore Civils (UK) to establish the cause and resolve the matter.
“The CJV has also assured us that it is making all payments to the firm in accordance with the terms and conditions of their subcontract.”
The £745m, 28-mile bypass project has been beset with problems and only last month the completion date was pushed back by another six months to the autumn.
When the contract was first let final completion of construction was anticipated in the second half of 2017, hailed at the time as shaving around 6 months off the original construction timescale.
The latest delay is being blamed on the impact of Storm Frank during winter 2015/16, recent extreme weather during early March and the collapse of third JV delivery partner Carillion.