Ministers must introduce a plan to tackle the inequalities before the end of the year, the MPs urged.
The government said it was committed to making Britain “work for everyone”.
“We are making progress – for example, there are now 45% more Muslim women in work than in 2011 – but we know there is much more to do,” the government spokesman added.
The committee suggested many Muslim women in Britain faced a “triple penalty” impacting on their job prospects – being women, being from an ethnic minority and being Muslim.
Evidence suggested the biggest cause of the “acute” disadvantage felt by Muslim women is their religion, it said.
“The impact of Islamophobia on Muslim women should not be underestimated,” it went on.
“They are 71% more likely than white Christian women to be unemployed, even when they have the same educational level and language skills.”
They face particular issues of discrimination when applying for jobs because of the clothes some of them they wear because of their religion or culture, the MPs suggest.
The report refers to a “chill factor” where the perception and fear of discrimination or hostile work colleagues puts Muslim women off applying for certain jobs.
A 21-year-old Muslim graduate from Manchester has spoken anonymously about what she believes was discrimination when she applied for a sales job.
She said: “There were two phone interviews… and I got brilliant feedback. They said ‘You sound absolutely perfect for this role’ and said I was very articulate – that kind of thing.”
But the 21-year-old said that when it came to a face-to-face group interview, during which she was the only person wearing a headscarf, there was a “change in the tone”.
“I felt they were strange, and there was a bit of a change in the atmosphere, and that was not a nice feeling for me,” she said.
She did not get the position.
“It has lessened my confidence a little bit when going for face-to face interviews, I definitely think I’m more confident over the phone,” she added.
The MPs called on ministers to roll out “name-blind recruitment” to all employers, so that recruiters do not see applicants’ names, following evidence that job applicants with white-sounding names are more likely to get an interview.
“Both the government and the Equality and Human Rights Commission must take action to make sure that employers are aware of their legal duties and employees are empowered to challenge discrimination,” the report also said.
Figures for 2015 suggest Muslim women are the least economically successful group in British society.
While 69% of British working-age women were in employment, among Muslim women it was 35%. Nationally, 5% of women were unemployed and seeking work but among Muslim women it was 16%.
The starkest comparison is in the proportion of women who are classed aseconomically inactive – that is, unemployed and not seeking work.
Among women generally, last year 27% were economically inactive. However, among Muslim women the figure was 58%.
Nearly half (44%) of economically inactive Muslim women are inactive because they are looking after the home; this compares with a national average of 16% of women who are inactive for this reason, says the report.
Married women in Muslim communities are often expected to be home-makers while their husbands are the breadwinners, the committee heard from expert witnesses.
“The impact of the very real inequality, discrimination and Islamophobia that Muslim women experience is exacerbated by the pressures that some women feel from parts of their communities to fulfil a more traditional role,” the committee said.
“The Equality Act applies to everyone and all women, regardless of faith, should be free to make their own choices about all aspects of their lives, including education, employment and dress, and subsequently be empowered to overcome the disadvantages they may face,” the report concludes.
Official figures suggest younger Muslim women are challenging traditional cultural roles but the MPs said change is happening too slowly.
“The government must introduce a plan to tackle the inequalities faced by Muslims by the end of the year,” the committee said.
Although in some local authorities Muslim women’s participation in higher education is now greater than that of Muslim men, the proportion unemployed and looking for work is significantly higher among females.
“We call on the Government to introduce a role models and mentoring programme aimed at Muslim women to help them realise their potential in employment,” the report said.
Maria Miller, who chairs the Women and Equalities Committee, said: “Muslim women particularly, face really unacceptable levels of discrimination and that discrimination comes from the workplace, from employers, but also from within communities as well.”