The bipartisan approval of the measure—over the objections of industry groups including

Meta Platforms Inc.’s

Facebook and

Alphabet Inc.’s

Google—provides momentum for this legislation and other bills aimed at overhauling Section 230.

“Our goal is to tell the social media companies, ‘Get involved and stop this crap,’ ” said

Sen. Lindsey Graham

(R., S.C.), a chief sponsor. “ ‘And if you don’t take responsibility for what’s on your platform, then Section 230 will not be there for you.’ And it’s never going to end until we change the game, and this bill changes the game.”

The bill heads next to the Senate floor, where opponents, including internet giants, with the aid of some privacy and human-rights advocates, aim to stop the measure, or slow its advance while alternatives are considered.

In a letter to lawmakers this week, a coalition of industry groups that also include

Amazon.com Inc.

and

Twitter Inc.

in their ranks say the legislation would “subject companies to litigation under an unpredictable patchwork of state laws.”

Section 230, adopted in 1996, generally exempts internet platforms for liability for third-party content posted on their sites. It has been credited with playing a crucial role in spurring the development of internet platforms by shielding them from lawsuits that might have stifled their growth.

The new measure would create an exception to the 1996 immunity law for child-sexual-abuse material. Under the bill, a platform could become liable for such material, generally in situations where the platform is put on notice that it is hosting the material and does nothing about it, sponsors said.

Lawmakers said the bill is an effort to address what

Sen. Dianne Feinstein

(D., Calif.) said is a “growing problem of sexual abuse of minors on the internet.”

In opposing the bill, tech groups have said that it could undermine platforms’ use of encryption technologies, encouraging them to weaken encryption to better police their sites and comply with the new legal standard. Bill sponsors dismissed that concern.

The bill is also opposed by a coalition comprising more than 60 privacy and human-rights groups. In a letter to lawmakers, these groups said that passage of the Earn It Act could lead platforms to “engage in overbroad censorship of online speech, especially content created by diverse communities, including LGBTQ individuals.”

The bill’s name is an acronym for Eliminating Abusive and Rampant Neglect of Interactive Technologies. Several lawmakers said they hope the measure is the beginning of a broader review of the immunity law.

“This approach is very narrowly targeted,” Sen. Richard Blumenthal (D., Conn.) said. “But I hope we will review Section 230 as a whole,” adding that it is “arguably a very unnecessary immunity we give to Big Tech.”

Corrections & Amplifications
An earlier version of this article referred to Meta Platforms Inc. incorrectly as Meta Inc. (Corrected on Feb. 10)

Write to John D. McKinnon at john.mckinnon@wsj.com