The Hill said the measure, which has the support of business leaders, is expected to be voted on by the full Senate before year's end.
The Washington publication noted the legislation would have the Commerce Department's National Institute of Standards and Technology work with businesses to set cybersecurity best practices and standards.
The bill doesn't deal with security standards for companies that operate critical infrastructure and improving information-sharing about cyberthreats, which The Hill said lay outside the committee's purview.
"Our bill takes some important steps to help our private companies and our government agencies to defend their networks against their adversaries," Sen. Jay Rockefeller, D-W.Va., the bill's co-sponsor, said prior to the vote. "It doesn't do everything we need to do to improve our cybersecurity, but it's a good start and I thank Senator [John] Thune [R-S.D.] for working with me on this urgent issue."