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."

Rob Davies, 32 from Brecon, and his fellow Welshmen won their first three matches in the round-robin stage.
In the final Italy won the doubles 3-2, but Matthews levelled the tie with a 3-1 win against Federico Falco.
Rob Davies then secured gold with 3-0 win against Andrea Borgato.
Elsewhere in the British Para Table Tennis Team, Aaron McKibbin and Ross Wilson took silver in the men's class 8.
Megan Shackleton, 18, and her Russian team partner Aleksandra Vasileva took silver in the women's class 4-5, and there were bronze medals for Paul Karabardak and Martin Perry in the men's class 6.
Further bronzes followed for Will Bayley and Billy Shilton in the men's class 8, and Ashley Facey Thompson and his German partner Yannick Ruddenklau in the men's class 9.
Find out how to get into table tennis with our special guide.

What is mental health?
Mental health is to do with how people think and feel, and how they are coping.
There are different types of mental health problems and they are treated in different ways.
It is perfectly normal to feel sad or worried from time to time, but if those feelings last a very long time or won't go away, this can be when there is a mental health issue.
In a speech on Monday morning, she said she wanted to make sure that "children and teenagers get the help and support they need and deserve".
She said one of the ways she wanted to do this was by helping schools to support pupils who might be having problems like anxiety or depression.
This will be done by:
â€¢Providing more training for teachers, so they know what to do if someone in their class is having problems
â€¢Help schools and colleges to link up with mental health experts in their areas, to make sure children have any support they might need
The prime minister also said that the UK government would be looking at the services that are available at the moment for children and teenagers, to see what is working and what isn't.
One of the issues is that people who have a mental health problem are not always treated in the same way as those diagnosed with a physical problem.
She said that, currently, the way people with mental health problems are treated is "inadequate".
For example, many children have to travel a long way from their homes in order to receive their treatment.
The prime minister said that by 2021, no child will have to do this anymore for a general mental health problem.
Overall, she said the government needs to do more to support people who may have mental health problems.
"[They] affect people of all ages and all backgrounds," she said.
"All of us need to do more to support all of our mental wellbeing."
Paul Farmer - the chief executive of Mind, which is a mental health charity - said it was "important to see the prime minister talking about [this]".
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.
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Paralympic table tennis gold medallist Rob Davies, Tom Matthews and Paul Davies beat world champions Italy to win gold in the men's class 1 team event at the German Open on Saturday.
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The UK's prime minister Theresa May has said she is going to provide more support to help young people who may be struggling with a mental health problem.