Schwesig's planned law would allow women to check their salary against those of men doing comparable work.
Employers reacted angrily to the plans in early March, saying that it would create a climate of mistrust among workers, but Merkel's support, which Schwesig confirmed she had in an interview on ZDF television, will likely ease its path through parliament.
The proposals were first mentioned in the coalition agreement signed in late 2013 between Merkel's Christian Democratic Union (CDU) and the Social Democratic Party (SPD).
Schwesig has said that she wants to put the law to a vote in the Bundestag (German parliament) this year. MPs are slated to debate the subject later on Friday.
Volker Kauder, parliamentary leader of the CDU for Bavaria, also declared his support for the proposals and called for employers to "look at their wage contracts closely in order to see if male and female employees are being paid fairly."
Although men and women should be paid the same wage by law, the average woman earns €5 less an hour than the average man, according to 2014 statistics.
This wage gap equates to 22 per cent, one of the highest in the EU.
While women often work part-time or lower-paid jobs, the pay gap between men and women with similar skills and qualifications is still 7 per cent on average, according to Family Ministry figures.
(Average pay gap between men and women in different German states and across Europe, in %)
Schwesig has pushed hard for the rights of women in the workplace, making herself the driving force behind a law requiring set numbers of women on the boards of large companies and in the civil service passed in early March.
Some good news for the SPD and women alike is that experts believe that the new national minimum wage of €8.50 an hour - one of the left-wing party's key demands for working with Merkel and the CDU - is having a positive effect on the pay gap.
"Women will benefit from the minimum wage because the majority of workers originally paid under €8.50 an hour are women", said Christina Klenner from the Institute of Economic and Social Research.
by Matty Edwards