The Resolution Foundation analysis shows the impact of the national living wage will vary considerably across Scotland.
A national living wage of £7.20 an hour for workers aged 25 and over will be introduced in April.
The UK government said millions of people will enjoy a pay rise.
The study said 500,000 employees in Scotland will be affected overall.
While one-third of employees in Clackmannanshire and Dumfries and Galloway will be affected, just 16% of employees working in Aberdeen are set to benefit.
Edinburgh (17%), Dundee (18%) and Glasgow (19%) are also significantly lower.
While strongly welcoming the new wage floor, the Foundation notes that implementing it will prove a greater challenge in lower-paying areas.
It calls on the Scottish government, the Fair Work Convention, local leaders and businesses across the country to work together to minimise any job losses and ensure large groups of workers do not get stuck earning only the legal minimum.
The Foundation also calls on employers to focus on boosting productivity in retail, hospitality, cleaning and care to ensure the national living wage is affordable for them.
The group states the UK government's new pay structure is not actually a "living wage", and calls for an expansion to the voluntary living wage of £8.25 across the country.
Conor D'Arcy, policy analyst at the Resolution Foundation, said: "The welcome new national living wage will have a huge impact on low pay, particularly towards 2020 as it approaches £9 an hour.
"While our analysis suggests the pay rise should be affordable for most firms, implementing the new wage floor will be challenging for some employers. That's particularly true in areas where wages tend to be lower.
"Politicians must work closely with employers to ensure that the national living wage is a success, particularly in low-paying sectors."
A UK government spokesperson said: "The government is making sure Britain gets a pay rise and that businesses have the skills they need to succeed. We are already seeing record employment rates and real wages growing to levels not seen since the recession.
"As the report itself highlights, workers in some cities will see even bigger benefits, reinforcing our drive to rebalance the economy through the northern powerhouse and the devolution of powers to local government and cities."

James Fairburn gave evidence to a Westminster committee on Tuesday.
In February, a consignment of beef being stored at Freeza Meats was found to contain horsemeat.
It did not belong to Freeza Meats and none of their products tested positive for horsemeat.
Mr Fairburn, who is now retired, said the beef belonged to another company, McAdam Foods, and that his firm has suffered.
He told MPs the scandal had led to his firm missing out on multi-million pound orders and had resulted in 31 jobs being lost in Newry.
Quizzed by MPs on the Environment and Rural Affairs Committee about the horsemeat scandal, Mr Fairburn described it as a "fraud" and said it was "being perpetrated by a big organisation".
He also said he suspected it had been "going on for some time".
He told MPs that the illegal meat trade originated in other parts of Europe and did not come from the UK or Ireland.
He rejected a suggestion from the Conservative MP Anne McIntosh that "all roads lead to Ireland".
Asked if the scandal originated in Ireland, Mr Fairburn said "not at all".
Mr Fairburn faced questioning from Conservative and Labour MPs and the South Down SDLP MP Margaret Ritchie.
MPs also heard evidence from the Food Standards Agency.
Tests carried out on the meat stored at Freeza Meats found that samples from the consignment contained about 80% horsemeat.
It followed the discovery of horse DNA at a plant in the Republic of Ireland.
Newry and Mourne Council confirmed that tests on Freeza Meats' burgers were free from horsemeat DNA.
Martin McAdam, whose firm owned the contaminated meat, said there was "clearly an issue" with their Polish supplier.
About one-third of workers in Clackmannanshire and Dumfries and Galloway will benefit from the national living wage, according to research.
[NEXT_CONCEPT]
The former director of a Newry food company which was at the centre of the horsemeat scandal has said his firm did nothing wrong.