The petition is currently the most popular of those posted at adressit.com.
Last week Räsänen, who is also the Christian Democrats’ party leader, told the regional newspaper Hämeen Sanomat that limiting bars’ opening hours would minimise street brawls that burden police.
“Bars want patrons to come in earlier. They say many of the customers arriving after midnight are already drunk,” wrote Räsänen in her blog on Tuesday.
Bars and restaurants have opposed the idea, saying it would hit jobs in the sector.
No stranger to controversy, Räsänen has drawn repeated public criticism for her conservative views on homosexuality.