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.

They controlled the game from the off, opening the scoring when Kyle Bennett fired home from 20 yards.
Michael Doyle hit the bar from range for the visitors, who doubled their lead when a Ben Davies cross was turned into his own goal by Matt Pearson.
Pompey's Doyle did score, volleying beyond Jason Mooney from 30 yards, before Shay McCartan pulled one back.
The result means Stanley are down to sixth, while Paul Cook's side are now six points off the final automatic promotion place.

No suspicious packages were found and passengers were being allowed back in the terminal buildings.
Earlier, flights were on hold after the airport received a "very specific threat" by phone at 14:00 (19:00 GMT).
Local news channel KENS 5 reported that one flight was diverted, three cancelled, and 28 delayed.
As the airport was reopened, officials warned there was heavy road traffic in the surrounding area.
While the airport was closed local news sources reported that dogs trained to detect bombs raised suspicions over three cars in an airport car park, indicating there could be explosives inside.
Airport officials confirmed that all three cars were eventually cleared.
Meanwhile, passengers were herded onto the runways, away from the airport buildings, before they were taken to a nearby high school while the search was under way.
About 2,000 passengers were cleared out of the airport during the evacuation, Fire Department spokeswoman Deborah Foster told the Associated Press.
The incident was brought to officials' attention at about 14:00, and the airport tweeted confirmation that it was evacuating the terminal buildings at 14:35.
San Antonio International Airport handles about 260 flights, carrying between 14,000 and 15,000 passengers each day, airport spokesman Rich Johnson said.
The spokesman said incoming planes landed they were directed away from the airport buildings.
Other planes were also asked to wait on runways, the spokesman said.

Stevenage goalkeeper Jamie Jones was tested by Rowan Liburd's header and Garry Thompson's strike from 20 yards.
Boro's Tom Conlon had a shot over the crossbar before Jason McCarthy missed the target and Liburd had more chances.
The winner came from McCarthy's shot rebounding to Luke O'Nien, who slotted home, while Stevenage almost equalised from 10 yards though Dean Parrett.
Stevenage remain in 21st, seven points clear of the relegation zone.
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.
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