The amendment, drafted by the top Democrat, Sen. Patrick Leahy of Vermont, passed on a vote of 16-4, with most of the committee's Republicans joining Democrats in support.
Added to an unrelated bipartisan bill addressing nuclear terrorism and maritime navigation, Leahy's amendment offers a "sense of the Senate" resolution that the U.S. won't bar entry because of religion.
"It is the sense of the Senate that the United States must not bar individuals from entering into the United States based on their religion, as such action would be contrary to the fundamental principles on which this nation was founded," the amendment reads.
Leahy noted he proposed the language in direct response to Trump's call earlier this week to ban entry to the U.S. to all foreign Muslims, which has been widely rejected by members of the both parties.
"Many on this committee have rightfully expressed their outrage about the call earlier this week to shut our borders to Muslims. Now we need to formally go on the record to reject this reprehensible position," Leahy said.
Sen. Jeff Sessions, R-Alabama, opposed the amendment, saying it "would constitute a transformation of our idea toward immigration" and impinge the ability of U.S. officials to make discretionary calls about who should enter the country.
"What this amendment would do would be to ... apply some of our core domestic legal and constitutional protections to foreign nationals with no tie to the United States," Sessions said, suggesting it could pave the way to factors like age, country of origin and criminal history being banned from consideration, as well.
But he was largely outnumbered, including by committee Chairman Chuck Grassley, R-Iowa.
Some of the strongest condemnation of Trump and support of the amendment came from California Democratic Sen. Dianne Feinstein.
"When I heard the leading candidate of the Republican Party step up and say he would ban one religion across the board ... I felt like somebody had shot me in the gut," Feinstein said.
She also mocked Trump's follow-up comments that, "'I'm the best friend Muslims will ever have' -- well that's just sheer hypocrisy," she said.
She acknowledged that "sense of the Senate" resolutions don't hold any legally binding power, but stressed the importance of the symbolism of the vote.
"This is the first time we have the opportunity to say to this candidate this is not what our nation stands for," she said as she urged her colleagues to support the amendment.
The four no votes came from Sessions, Texas Republican Sen. Ted Cruz, Louisiana Republican Sen. David Vitter and North Carolina Republican Sen. Thom Tillis.
Cruz, who is also running for president, has been the most reticent to criticize Trump, but has said he does not advocate Trump's Muslims proposal.
To become law, the bill the amendment is attached to would have to pass the Senate and the House and be signed by the President.