The "Slap Hillary" site "isn't a game, it isn't funny," Pelosi wrote in a Twitter message. "Like all violence against women, it's sick. GOP needs to grow up and take this site down."
The website is paid for by The Hillary Project Political Action Committee, according to a notice on the site.
The site said its goal is to collect 200,000 signatures online to persuade Clinton not to run for president in 2016.
"Hillary Clinton - the name alone strikes dread in the hearts of freedom loving Americans," the site states. "Can you imagine what damage a Hillary White House could do to our country? Our constitutional rights upended, our moral values eroded and taxes eating up more and more of our paychecks."
The site asks signers of the petition for their first and last names, email addresses and zip codes.
The site also includes a Dancing Hillary game and a game featuring a fight between Clinton and President Barack Obama.
The site identifies itself as operating out of an office on Amherst Street in Nashua, N.H.