The students, most of whom were in their school uniforms, carried placards reading: “Afrikaans stinks”, “To hell with Afrikaans” and “Afrikaans needs to be abolished”.
Dan Montsitsi, a student leader of the uprising, said the maiden Soweto march had been planned for months.
“We were amazed with the number of students that we had been able to put in the streets,” he told AFP.
He added that the shooting started after police released a dog into the crowd, which was killed.
“The police were very angry obviously and they decided they would use teargas,” he said. “(Soon after) they started to shoot.”
Deputy President Cyril Ramaphosa, who is widely expected to take over from Mr Zuma, placed a wreath at the memorial to Hector Pieterson, who was killed aged 13.
The aftermath of his shooting was captured in black and white by local photographer Sam Nzima and beamed around the world. It was credited with helping to raise pressure and bring about trade blockades on the apartheid regime that led to its downfall.