They told the BBC they went to the embassy as there was no security for them in the capital city Bujumbura.
Social media has been blocked, radio stations closed and protests banned.
People have been protesting since Sunday over President Pierre Nkurunziza's decision to stand for re-election in June.
African news at it happens: 1 May 2015
The government closed the university on Thursday citing "insecurity".
Earlier on Thursday several hundred students tried to organise a march into the centre of Bujumbura. They wanted to stop the president from officially presenting his nomination papers to the electoral commission.
The students told the BBC's Maud Jullien that the US embassy was the only place they felt safe and that they feared security forces were pursuing them.
She estimates around 500 students are outside the embassy.
The US has not reacted to their presence.
Senior US diplomat Tom Malinowski met Mr Nkurunziza on Thursday, and afterwards said he had warned that the situation in Burundi was "dangerous".
"Some of the measures that have been taken... to shut down social  media, to suspend radio stations not only are wrong as a matter of principle  but very counter-productive," he told journalists.
Rupert Colville from the UN human rights office also said on Friday that he was "deeply concerned" about the authorities' curtailing people's freedom of speech.
At least seven people have died amid the biggest protests Burundi has seen since the civil war ended in 2005.
In a Labour Day radio broadcast Mr Nkurunziza, a former rebel leader, warned of "severe sanctions" against protesters who are found to be behind an "insurrectional movement".
President Nkurunziza said there would be a judicial inquiry into the protests.
Under the constitution, presidents can only be elected to two terms in office but Mr Nkurunziza's allies say his first term does not count as he was appointed by parliament.
Burundi's senate has announced that the constitutional court will examine the legality of the bid.
Mr Nkurunziza has been in power since 2005, when a 12-year civil war officially ended.
More than 300,000 people died in the conflict between the minority Tutsi-dominated army and mainly Hutu rebel groups, such as Mr Nkurunziza's CNDD-FDD.

South Korea's new President Moon Jae-in backed proposals for a collaboration after it was suggested by sports minister Do Jong-hwan.
But North Korean International Olympic Committee (IOC) member Chang Un has dismissed the idea - saying there was not time to negotiate a deal.
The Games in Pyeongchang, South Korea, will take place from 9-25 February.
The two sides have played in the same team before - at the 1991 World Table Tennis Championships.
However, Mr Chang told local media: "It took us 22 rounds of talks to set up that joint [table tennis] team... it took us five months.
"That's the reality we face."
South Korea's sports minister had suggested a joint ice hockey team - even going as far as to suggest they might allow the north to host skiing events - to help make the 2018 games a "peace Olympics".
President Moon, who advocates greater dialogue with South Korea's neighbours, then put forward the idea of a wider unified Olympic squad.
But Mr Chang said the games should not be used for political purposes, adding: "As an expert of the Olympics, it is a little late to be talking about co-hosting. It's easy to talk about co-hosting, but it is never easy to solve practical problems for that. It's the same for forming a joint team for ice hockey."
South Korean officials have said they continue to be open to the idea.
The two sides remain technically at war as the fighting at the end of the Korean War in 1953 did not end with a peace treaty. Tensions have risen recently following repeated missiles tests carried out by Pyongyang.
Hundreds of students in Burundi have spent the night in front of the US embassy after their university was closed amid anti-government protests.
[NEXT_CONCEPT]
North Korea has rejected an offer from the South to form a unified team for next year's Winter Olympics.