The 11 members of the cross-party Home Affairs Committee will use their findings to inform recommendations to the government.
Labour MP Yvette Cooper, who chairs the committee, said too often only the "loudest, angriest voices" were heard.
She said immigration would be central to the Brexit deal.
Immigration to the UK rose to a record level with 650,000 migrants in the year to June, Office for National Statistics figures released earlier this month showed.
There was also a record number of EU citizens coming to live in Britain, 284,000.
While net migration - immigration minus emigration - stayed near record levels, at 335,000.
Launching the inquiry on Thursday, Ms Cooper told the committee: "There has been a lot of noise about immigration.
"Too often all that gets heard are the loudest, angriest voices and others are silenced.
"Some people exploit public concern to whip up fear and hatred.
"But just because some people exploit the issue in a way that is totally wrong, [that] doesn't mean the rest of us should be silent from talking about it or ignore the problem.
"It is not racist to worry about immigration.
"We have to make sure we have a sensible debate."
Earlier, Ms Cooper told the BBC's Breakfast programme: "People really need a say on what kind of reforms people want to immigration.
"For too long successive governments have failed on immigration, and public concern has just gone up.
"We should be having a really honest debate all round the country about what sorts of reforms, what kinds of controls people want to see."
She said the government would be "crazy" not to listen to what people were saying about immigration.
"If we don't get a consensus around the final Brexit deal, it will unravel," she added.
The committee plans to hold public meetings, debates and online consultations.
They are also encouraging community groups, business organisations, faith groups, think tanks and local councils to run their own debates.
A group of MPs are to hold public meetings across the UK to hear people's views on immigration and how it should be handled after the UK leaves the EU.