Footage showed protesters surrounding the van and hitting it with batons taken from police. The vehicle then drives into the crowd several times, injuring a number of people.
Hundreds had met to demand the US end its military presence in the country.
President Rodrigo Duterte has queried long-standing ties with the US.
Duterte in China: Conciliator-in-chief?
Police arrested at least 23 people, who threw red paint at them and a member of the US forces at the embassy.
Tear gas was used against the demonstrators, after they broke through a line of riot police. They also took control of the water hose of a fire truck being used to douse them and threw stones at police.
It remains unclear how many people were injured by the police van and how serious their injuries are.
Television footage of the incident shows the van driving into people at speed. At one point it knocks over a woman and drags her body along the road. The van brakes and she appears to scramble away.
Renato Reyes of the left-wing activist group Bayan said at least three people were taken to hospital after being rammed by the van.
"Even as the president avowed an independent foreign policy, Philippines police forces still act as running dogs of the US," he said, adding there was "no justification" for the police violence.
A spokesperson for the US embassy told the BBC it had "seen reports" of injuries, but declined to comment further, directing inquiries to police.
President Duterte is in Beijing, seeking to deepen ties and economic relations with China. Bilateral relations were strained under his predecessor over acrimonious territorial disputes in the South China Sea.
Relations with the US, a longstanding ally, have deteriorated in recent months over Mr Duterte's controversial war on drugs.
The US has questioned the crackdown, which has led to the deaths of 2,300 people. In response, Mr Duterte has insulted US President Barack Obama and the US ambassador to the Philippines.
A police van has rammed protesters in the Philippines capital Manila as a demonstration outside the US embassy turned violent.