A revised scheme will come into effect in October, so that any employer who breaks minimum wage law can be named.
Under the current arrangements, employers have to owe at least £2,000 to workers, at an average of £500 per employee, before being referred to HM Revenue and Customs for naming.
More than 730 employers were found to have failed to pay the statutory minimum in 2012/13, leading to the recovery of £3.9 million in unpaid wages for 26,500 workers.
Employment Relations Minister Jo Swinson said: "Paying less than the minimum wage is illegal. If employers break this law they need to know that we will take tough action.
"This is why I'm making changes so it is easier to name and shame employers who break the law. This gives a clear warning to rogue employers who ignore the rules that they will face reputational consequences as well as a fine if they don't pay the minimum wage."
The move will be welcomed by unions, who have complained that too few people have been named for failing to pay the minimum wage.
"At the moment all employers who have been found guilty of cheating workers out of a legal wage have to pay a financial penalty but, as this takes place behind closed doors, justice is not seen to be done.
"But naming and shaming won't be enough to deter those employers who think they are above the law.
"Only a handful of employers have been taken to court since the minimum wage was introduced in 1999, yet over the years thousands of workers have complained to the minimum wage helpline that they are being ripped off.
"Employers need to know that there will be no hiding place if they break the law. The Government must put more money into enforcement so that there are fewer places for even the most determined minimum wage cheats to hide."
Paul Kenny, leader of the GMB union, said: "Allowing unions to report companies not paying the national wage to HMRC would be another useful step in securing better enforcement as now the workers have to run the gauntlet on this and employers are not slow in victimising them."