The MP was suspended by Labour last week and apologised to the Commons for endorsing calls in 2014 for Israel to be moved to the United States.
The comments triggered a wider row over alleged anti-Semitism within the party, with an inquiry now under way.
Keith Vaz, the chair of the committee, said Ms Shah would not take part in its meetings for the time being.
The committee is beginning an inquiry into the extent of anti-Semitism in the UK and will call Labour leader Jeremy Corbyn and Ken Livingstone, the former mayor of London who was suspended from Labour for suggesting Adolf Hitler was a Zionist, among its witnesses.
Mr Vaz said Ms Shah - the MP for Bradford West who was elected to Parliament in May 2015 - had requested not to be involved in this inquiry or the committee's other activities for the time being.
"Naz Shah has informed me and the committee that she wishes to stand aside from all her duties until current matters are resolved," he said.
"We have accepted her decision. She will not take part in any future matters concerning the Home Affairs Select Committee with immediate effect."
Mr Corbyn has asked the former head of Liberty, Shami Chakrabarti, to lead an inquiry into the extent of anti-Semitism and "other forms of racism" in the party. No timeframe has been given for when its findings will be published.
Ms Shah told MPs last week that she regretted a series of Facebook posts in April 2014, including one endorsing a suggestion that Israel should be relocated to the United States as a "solution" to the Israeli-Palestinian conflict.
Ex-Labour MP Naz Shah has "stood aside" from the Commons Home Affairs select committee "until further notice".