Those affected include President Ashraf Ghani's picks for the key posts of interior and foreign affairs ministers.
Afghanistan's new cabinet was unveiled last week after three months of wrangling over last year's bitterly disputed presidential election.
The agreement to form a "national unity government" was seen as key to resolving the impasse between poll rivals Ashraf Ghani, who eventually won, and Abdullah Abdullah.
The deal was credited with steering the country away from possible civil war after both candidates claimed election victory in a stand-off that fanned long-standing ethnic tensions.
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"It is because in the past, those with dual citizenships fled the country easily after committing crimes or corruption and we had no access to bring them back," MP Sadeqizada Neli told AFP.
Those affected include Noorul Haq Ulumi, nominated as interior minister, Salahuddin Rabbani, nominated for minister of foreign affairs and Aisultan Khairi, one of three women in the cabinet, nominated for the post of minister of information and culture.
The other nominees disqualified are nominees for the ministries of social and labour affairs, urban development, justice and counter-narcotics, according to MPs.
Shekiba Hashimi, another MP, told AFP the nominees had until Sunday to renounce their dual status.
Humaira Ayoubi another MP said the lawmakers have asked the president to introduce new nominees to replace those with dual citizenships.
Last year's presidential election, which was meant to be the keystone legacy of the massive international development effort in Afghanistan, was marred by fraud and bitter disputes over the result.