The Democratic presidential nominee said the US leader views the situation as “a political benefit.”
Speaking just hours before Mr Trump’s planned address on the final night of the Republican National Convention, Mr Biden said: "He's rooting for more violence, not less.”
He had been largely silent during the first three days of the Republican convention, during which Republicans have warned a Biden presidency would make America less safe.
The police shooting of Jacob Blake in Kenosha, Wisconsin, once again sparked protests against racial injustice and police brutality.
Days after Sunday’s incident, a 17-year-old was arrested in connection with the fatal shooting of two protesters in clashes between vigilante militias and demonstrators.
White House adviser Kellyanne Conway suggested on Fox & Friends that the Wisconsin unrest could help Mr Trump's re-election chances.
"The more chaos and anarchy and vandalism and violence reigns," Ms Conway said, "the better it is for the very clear choice on who's best on public safety and law and order."
Mr Biden does not support defunding the police, as Republicans have erroneously suggested.
Instead, he has advocated for overhauling US police practices after years of high-profile killings of black Americans by officers.
Kamala Harris, the vice presidential nominee, defended the protesters in remarks sure to give fuel to Mr Trump on the convention's final night.
"It's no wonder people are taking to the streets - and I support them," she said. "Make no mistake: we will not let these vigilantes and extremists derail the path to justice."
Mr Biden, who has largely limited travel to near his home in Wilmington, Delaware, during the pandemic said he would consider travelling to Kenosha.
"If I were president I'd be going," Mr Biden said. "But it's hard to tell now what the circumstance on the ground is."
Should he make the trip, Mr Biden said, he would attempt to "pull together the black community as well as the white community and sit down and talk about how we get through this".