Image copyright Reuters Image caption Miss Tlaib said she “won’t be playing” in 2022.
Democrats became the first majority party to pass a bill to phase out private prison contracts, the US House of Representatives said.
More than 130 Democrats, mainly from the minority party, voted for the legislation.
A close Democratic ally of Congressman Keith Ellison – who is also the co-chair of the Congressional Progressive Caucus – asked her tough questions during the debate.
Incumbent Ilhan Omar was forced to apologise for shouting “Allahu Akbar” during the debate.
She was accused of Islamophobia and a “double standard” after the image, which showed the phrase written in Arabic on a street sign, was circulated on social media.
The Minnesota Democrat responded by saying “Allahu Akbar” has no relation to terrorism and was shouted by a man who lived in a building next to her, according to KSTP-TV.
Miss Tlaib said she “won’t be playing” in 2022 and questioned Ms Omar’s claim to represent the voice of Muslims.
“I know I won’t be playing in 2022 but right now we’re trying to grow.”
Speaking to BBC News, she said the vote had taken place because “a lot of us were not happy with the choices that ICE (Immigration and Customs Enforcement) had made”.
That statement referred to the recent policy of separating children from their parents at the US border.
A statement from the House Democratic Caucus said it was time to “make a transition”.
The Trump administration has said private prisons should not be used to detain undocumented immigrants.
Under the bill – which still needs Senate approval – the US government would spend an additional $2.9bn (£2.2bn) on minimum-security jails or prison units that have beds for fewer than 700 people.
A Department of Corrections’ official said the bill would result in a nearly 60% increase in the number of prisons available for inmates.
Miss Tlaib, 33, who won her congressional seat last year, is the first Muslim woman in the US House of Representatives.