Some critics contend the winners are pre-determined. Others complain that they take money away from casinos and charities that offer gambling and are strictly regulated.
It's unclear whether the state Senate will approve the bill before the legislative session ends this year.
Senate President Tom Niehaus told reporters Wednesday that he planned to review the bill. "We're going to take a look at it," he said. "I don't know what's in it, but we are going to take a look at it."
Niehaus said a week ago that he was more inclined to favor regulation rather than an outright ban.
Charities and fraternal organizations such as the Veterans of Foreign Wars that offer gambling and must give a share of their profits to charity have argued that the Internet cafes should at least play by the same rules.
William Seagraves, executive director of VFW of Ohio Charities, said Internet cafes been a big reason why the groups' charitable contributions from gambling have dropped from $6 million a year to $3.8 million since 2005.
"They kill us," he said. "They're just running wild. I'm hoping they get rid of them because it really hurts us."