The rate for the three-month period ending in March rose from 12.6 percent in February.
It means there are now 13.7 million people officially out of work, the Brazilian Institute for Geography and Statistics said.
Compared to the last quarter of 2017, when unemployment dipped to 11.8 percent, there are now 1.4 million more people without jobs.
The 13.1 percent rate is still below the peak of 13.7 percent recorded in the same period a year ago, but it comes as bad news for conservative President Michel Temer's unpopular government.
The worst recession on record in Latin America's biggest economy saw unemployment shoot up from just 6.5 percent at the end of 2014 to the high of 13.7 percent a year ago, before steadily declining.
This year's gradual reversal of that improving trend throws a question mark over the depth of the recovery which is expected to grow 2.3 percent this year, according to the IMF.