She was seen by some as a future leader of the National Front (FN), founded by her grandfather Jean-Marie Le Pen.
She said she was giving up because she missed her two-year-old daughter but was not leaving politics for good.
Her aunt, Marine Le Pen, won just under 34% in the presidential run-off.
She said she regretted her niece's decision, but - "as a mother" - she understood why she had taken it.
"As a political leader I deeply regret Marion's decision, but, alas, as a mother I understand her"
In a letter to her local newspaper in the south-eastern Vaucluse area, Marion Maréchal-Le Pen, 27, explained her decision not to defend her role as one of only two FN MPs in the National Assembly.
She is also leaving her position as president of the FN in the wider Provence-Alpes-Côte d'Azur region.
'Not giving up'
Ms Maréchal-Le Pen said she had not spent enough time with her daughter "in her very precious early years - and I have missed her terribly, too. It's vital that I devote more time to her".
At the same time she said politics had been her whole life and she did not rule out a comeback: "I'm not giving up the political fight forever."
She loved the world of business, she added. And if she was going to make a good political boss, then she should take advantage of experiences beyond politics.
Her decision is seen as a blow to the far right, which attracted 10.6m votes on Sunday, its biggest vote on record.
The FN is now hoping to translate that advance into a larger number of seats in parliamentary elections on 11 and 18 June.
The party's presidential candidate, Marine Le Pen, has been widely criticised for a series of failings in the final weeks of the campaign, particularly her abrasive performance in the televised pre-election debate.
Marion Maréchal-Le Pen is more hardline than her aunt, who tried to attract a broader range of voters with a greater focus on social policies.
After the election, the young MP admitted to being disappointed by the result, and said the party needed to reflect.
Jean-Marie Le Pen denounced his grand-daughter's decision to step back from politics as a "desertion", as she represented the future for many FN supporters.
14 May: President François Hollande formally hands over power to Emmanuel Macron
15 May Mr Macron will name his choice of prime minister
15-19 May: The new president finalises candidates for his party in the parliamentary election
11 and 18 June: Parliamentary election held over two rounds. All 577 seats are being contested