Riot cops wanted to prevent demonstrators from moving from the spot where they were gathered at one end of the city's major Paulista Avenue, an AFP reporter at the scene said.
That caused a stampede by the mainly young demonstrators, most of whom were gathered peacefully. Some had their faces covered.
Television pictures showed some demonstrators who were injured.
The military police in the city said on Twitter that two people were arrested with "explosive devices".
Many Brazilians are enduring hardship in a recession in the world's seventh-biggest economy.
The city government says that the rise in the price of a bus or train ticket from the equivalent of USD 0.80 to about USD 1.00 is less than the rate of inflation.
It was the second day of protests after similar demonstrations on Friday in Sao Paulo and other cities including Rio de Janeiro, which hosts the summer Olympic Games in August.
The incidents prompted memories of the riots that struck Brazilian cities in mid-2013 and, on a smaller scale, in mid-2014.
"I took part in the protests in 2013 and they had an impact on the city," said one demonstrator in Sao Paulo, 20-year-old student Helena Goncalves.
"I hope that the same will happen this time.
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