Some 5.4 million people are eligible to vote in the polls in Emilia-Romagna, a wealthy central region, and southern Calabria, Italy's poorest.
Renzi, the 39-year-old former mayor of Florence who became prime minister last year, initially enjoyed wide praise for his dynamic, modern style, but his popularity has been eroded by the economic crisis, unemployment and social tensions.
Trade unions are up in arms over Renzi's planned reforms to the job market, which critics say will stamp on workers' rights.
Italy is teetering on the brink of a third recession in six years.
Polls closed at 2200 GMT and results will be announced on Monday.