Many leading Democrats have called on Biden to choose a woman of color to round out his ticket, especially after the nationwide Black Lives Matter-inspired protests that followed Floyd's death. "If you want to heal this nation right now - my party, yes, but our nation - this is sure a hell of a way to do it".
Ms Klobuchar said the Democratic nominee should choose a woman of colour as the vice-presidential candidate.
Just reading the political zeitgeist, and what Biden has said about what he is looking for, with Klobuchar (who was a clear internal favorite) fully out, it feels like a Biden-Harris ticket is more and more likely every day.
Ms Klobuchar's chances of getting as Mr Biden's running mate diminished after the killing of George Floyd by a white police officer in Minneapolis.
"After what I have seen in my state, what I have seen across the country, this is a historic moment", Klobuchar said. "With your help, we're going to beat Donald Trump", Biden said. On Thursday, she took her name out of the running.
Shortly after Klobuchar made her announcement Biden reacted on Twitter.
The police custody death of George Floyd last month, a black man who died after a white officer kneeled on his neck for almost nine minutes in Minneapolis, had already complicated Klobuchar's case to be Biden's pick as her record as a Minnesota prosecutor came under new scrutiny.
Amy Klobuchar isn't falling on the sword, she's stabbing Elizabeth Warren in the back with a dagger.
Klobuchar said she sees an important role for herself in the Senate in pushing legislation to respond to the questions and concerns raised anew by Floyd's death.
In addition to a small group of family and advisers, Joe Biden is relying on two-term Congresswoman Lisa Blunt Rochester, the first woman and African American elected to Congress in Delaware's history, whom he called on months ago to help choose his running mate.
Top VP options include Senator Kamala Harris, Congresswoman Val Demings, and Obama-era national security advisor Susan Rice.