The material is to be transported by road from the nuclear power complex to Scrabster harbour for shipping to Sellafield in Cumbria.
A nine mile (14.4km) stretch of the A836 would be involved.
Dounreay is being decommissioned and tonnes of its radioactive material is being reprocessed at Sellafield.
Other items have been taken to the Cumbrian nuclear site by train, and also flown to the US and shipped to Belgium.
Dounreay said the removal of the latest material formed part of a new phase of the clean up of the site near Thurso.
A spokesperson for Dounreay said: "Dounreay is being demolished, so nuclear materials are being returned to national stocks.
"This programme started in 2001 and is expected to take several more years to complete.
"Our priority at all times is to comply with regulations designed to ensure the safety and security of nuclear materials, both while in storage and transit."
The A836 forms part of the North Coast 500 (NC500) tourist route.
Tom Campbell, managing director of the tourism initiative, said: "The North Coast 500 is based on roads where people live, work commute as well as visit and enjoy the north Highlands and these roads, like all roads are subject to closures, roadworks and diversions.
"The nine mile stretch represents less than 2% of the NC500 and our understanding is that actual closures will be rare and infrequent."
A stretch of road in Caithness is to be closed for short periods on occasions over the next 12 months so nuclear material can be moved from Dounreay.