The idea of the committee was put forward by Holocaust survivor and life senator Liliana Segre in response to a regular stream of abuse hurled her way on social media.
The ruling 5-Star Movement and center-left Democratic Party (PD) backed the motion, but the far-right League and its allies, the Brothers of Italy and former prime minister Silvio Berlusconi's Forza Italia, all abstained.
"The abstention of some parties is a bit dismaying. It's a decision that we consider wrong and dangerous," said the president of Rome's Jewish community, Ruth Dureghello.
The Vatican's powerful number two, Cardinal Pietro Parolin, also weighed in.
"I am worried, in the sense that on some things like fundamental values we should all be united," he told reporters. "There is a danger that all this gets politicized. We need to break clear of this," he said.
Segre was deported from Italy to Auschwitz in 1944 when she was 13 - one of some 776 Italian children under the age of 14 who were sent to the Nazi concentration camp. Only 35 survived.
She said this month that social media haters posted an average 200 messages a day against her. "They should be pitied or treated," she said this week.
The League and its allies said they abstained in Wednesday's vote because Segre's motion was ambiguous, in citing, for example, nationalism and ethnocentricity as possible driving forces behind racial hatred.
"By doing that you are outlawing Brothers of Italy," said one of the party's senators, Giovanbattista Fazzolari. "This is not a commission on antisemitism, as they want you believe, but rather a commission aimed at political censorship."
While Brothers of Italy and the League, led by Matteo Salvini, have both positioned themselves on the far-right of the political spectrum, Forza Italia sees itself as center-right and some of its leaders were dismayed by the decision to abstain.
"We are betraying our values and changing our skin," said lawmaker Mara Carfagna, who is widely seen as a possible party leader when Berlusconi finally steps away from the helm.
She has voiced alarm at Berlusconi's recent efforts to patch up differences with the League and hand effective control of the rightist bloc to Salvini. "We are being dragged along without defending our identity," Carfagna wrote on Twitter.
The rightist bloc triumphed in a local election in Umbria on Sunday, beating a candidate put forward by the PD and 5-Star by 20 percentage points and ousting the center-left from power in the central Italian region for the first time in 50 years.
The Senate committee will be set up despite the abstention from the rightist bloc, but the 5-Star and PD both denounced their stance."This abstention seems to legitimize a culture of hatred that is reflected in society. It is a shameful page in our political life," said 5-Star lawmaker Elisa Tripodi.