Employers could be asked to pay up to £20,000 if they fail to provide the minimum £6.31 an hour for staff aged 21 or older.
Currently employers face penalties of up to £5,000 and possibly having their name published publically by the Government, after it launched a revised NMW naming scheme in October last year.
Intern Aware has campaigned for tighter controls over the NMW to ensure employers currently offering unpaid internships are forced to offer interns a fair wage.
Co-director Gus Baker said he was pleased about plans to increase fines, but warned they would only be affective if actually enforced.
“Last October we saw employment relations minister Jo Swinson announce the relaunch of the name and shame scheme about minimum wage enforcement,” said Baker. “I’ve been asking the Government about how many employers have been named under that scheme four months later, and I’ve been told it's zero.
“It’s good that the Government is increasing penalties for employers that break the minimum wage. However, often HMRC’s and the Department for Innovation, Business and Skill’s (BIS) bark is worse than their bite,” he continued.
“Not enough enforcement action is undertaken and companies are often allowed to get away with breaking rules on the NMW. Bigger fines are good but having any enforcement action is better.”
Fines should make employers 'think twice'
A report published by think tank Centre for London in December estimated that 300,000 workers in Britain are paid below the legal minimum rate.
TUC general secretary Frances O’Grady said the higher penalties “should make employers think twice before illegally underpaying their staff”.
“It’s great that the penalties for flouting the minimum wage have been raised and that it’s easier to name and shame offending employers,” she said.
“It’s crucial now that HMRC is given the resources they need to enforce these new rights properly.”
Business secretary Vince Cable said: "Anyone entitled to the minimum wage should receive it.”
"Paying anything less than this is unacceptable, illegal and will be punished by law. So we are bringing in tougher financial penalties to crack down on those who do not play by the rules. The message is clear: if you break the law, you will face action."
BIS said it hopes to introduce the change as soon as possible.