The Labour leader said the black community must have “trust and confidence” in the police following the incident on Sunday.
Ms Butler, who recorded a video of the incident, said she and her friend, who is also black, had been pulled over by Metropolitan Police officers simply for “being black and driving a nice car”.
SIr Keir tweeted: “I reached out yesterday to Dawn Butler to discuss the incidence she reported and to offer our support.
“All allegations of racial profiling must be taken extremely seriously by the Metropolitan police.
“It is imperative that the Black community have trust and confidence in our police.”
He also said the abuse Ms Butler received over social media since speaking out was “wrong and must be condemned”.
She has since accused officers of racially profiling her and said there was “institutional racism” in the police.
Scotland Yard said the stop was a result of an officer having “incorrectly entered” the car’s registration plate into a computer to wrongly identify it as a vehicle registered to Yorkshire, but did not explain why the search was carried out in the first place.
Earlier today, Ms Butler said she had been the victim of “racist trolls” online after speaking out about the police stop.
Twitter users claimed that her friend, who was driving, was white. Ms Butler, the MP for Brent Central, in north west London, said this morning that was not the case.
She tweeted: “Good morning twitter I see the racist trolls are going crazy with conspiracy theories.
“Someone who claims to be an ex police officer is challenging me to a debate.
“No need waste my time as I’m speaking to current police officers. Working together to make the system better.”
Ms Butler’s footage of the stop showed an officer saying police were carrying out searches because of “gang and knife crime”.
Ms Butler told the officers: “It is really quite irritating. It’s like you cannot drive around and enjoy a Sunday afternoon whilst black, because you’re going to be stopped by police.”
In the video, one officer says the initial search returned a car of the same make, model and colour but registered to North Yorkshire. Ms Butler was sceptical of this, asking for the police to share the registration they initially searched for to see how it returned such a similar car.
This week Ms Butler was named by Vogue magazine as one of the 25 most influential women shaping 2020 for her support of Black Lives Matter protests.
She described her backing of the anti-racism movement as having led to threats of attack on her office and staff having “drastically escalated”.
A Scotland Yard statement said: “Once the mistake was realised the officer sought to explain this to the occupants, they were then allowed on their way.”
The Prime Minister’s official spokesman said he did not share Ms Butler’s view that the met was “institutionally racist”.
He added: “No, I don’t think the PM would take that view of the Metropolitan Police.
“The Met, like police forces across England and Wales, are working very hard tackling issues such as knife crime and drugs.”