Eight percent of workers entitled to the prescribed minimum wage at the time - €8.50 per hour - did not receive it, the Economic and Social Sciences Institute (WSI) at the Hans Böckler Foundation has said.
Companies without workers' councils and collective labour agreements frequently undermined the minimum wage, added the WSI, an institute close to the unions.
In such companies, 18.6 percent of employees did not receive the legally prescribed minimum wage. By comparison, 3.2 percent of companies with workers' councils and collective labour agreements evaded paying workers the living wage in 2016.
The study also found that violations of the law were particularly frequent in industries involving small businesses and mini-job positions. Around 43 percent of employees in private establishments received less than the living wage. In the hotel and catering industry, this 2016 figure was 38 percent and in the retail sector 20 percent.
In response to the study, the largest social association in Germany, VdK, has demanded that stricter compliance controls be set in place and loopholes in the payment of wages be closed.
Last year, companies which failed to comply to such rules had to pay fines of more than €4.2 million, according to the Federal Ministry of Finance. Customs in 2017 also initiated about 2,500 investigation proceedings into businesses; in every second case a company had to pay up.
But the German Institute for Economic Research (DIW) has arrived at a significantly lower figure than the one in the WSI study. According to DIW, 1.8 million employees were deprived of the minimum wage in 2016.
The WSI study moreover indicated positive results in that it showed an improvement in the income of low-paid workers. The proportion of employees with an additional entitlement to German unemployment benefit Hartz IV fell from 20 percent in 2014 to 17 percent in 2016.
The minimum wage was implemented in Germany in 2015. As of January 2017, the minimum wage has been €8.84 per hour.