The Democratic congresswoman from Michigan said the shooting by Minneapolis officer Kim Potter "wasn’t an accident" and that policing in the United States was "inherently and intentionally racist".
"Daunte Wright was met with aggression & violence. I am done with those who condone government funded murder," she said in a tweet.
"No more policing, incarceration, and militarization. It can’t be reformed."
Asked if the Biden administration "disavows" Ms Tlaib’s calls to end the practice of policing, press secretary Jen Psaki said the president does not share her position.
"That’s not the president’s view," Ms Psaki said.
"The president’s view is that there are necessary outdated reforms that should be put in place, that there is accountability that needs to happen, that the loss of life is far too high, that these families are suffering around the country, that the Black community is exhausted from the ongoing threats they feel."
Former vice presidential candidate Tim Kaine pushed back on the suggestion in an interview with Fox News, saying there needed to be "reforms in the space of qualified immunity".
"But I am not in the camp that says, you know, we should disrespect police. We should reform police where police are necessary," the Democratic senator said.
Senator Ted Cruz said the idea of no more policing was "insane", posting to Twitter that it "doesn’t get more explicit than this that Democrats want to abolish the police".
Renowned pollster Frank Luntz said Ms Tlaib’s "no more policing" tweet would be bookmarked by lots of Republican campaigns for the 2022 midterm elections.
"For when Rep Tlaib claims she actually doesn’t want to abolish the police," he said in a tweet, highlighting only 15 per cent of Americans support abolishing the police.
"Emo-tweeting wasn’t a good look when Trump did it, and it still isn’t good when a Member of Congress does it – no matter how good the engagement is."