The people staged a protest against the third term bid of the country’s president, Pierre Nkurunziza, when two of them were killed by the Burundian police and four injured, the Red Cross said.
Police reportedly dispersed the protesters in Bujumbura with water cannon, tear gas and in some cases live bullets.
The government had banned all protests, pro or anti Nkurunziza's third term rerun.
According to reports, the law of the land stipulates that a President can only serve two terms, which makes a third attempt a violation of the constitution.
African leaders and Western nations have urged Nkurunziza not to run again.
The United States and the European Union have said they could take punitive steps if violence erupts as a result of the president's rerun.
"We counted two protesters killed by police, four others were injured and one is in coma in hospital after being hit by a bullet," Alexis Manirakiza, Burundi Red Cross spokesman said.
Burundi's ruling CNDD-FDD party nominated Nkurunziza as its presidential candidate on Saturday, April 25.
Critics say the move goes against the spirit of a 2000 peace deal. The peace deal has kept Burundi calm for a decade since a civil war between ethnic Hutus and Tutsis ended in 2005.