The protesters got within about 2 kilometers (1.5 miles) of the Maracana stadium on Friday. As they tried to get closer, security pushed them back, setting off clashes, AP reported.
Television footage showed two protesters setting fire to a yellow shirt carrying the logo "Rio 2016" and worn by staff working at the Olympics.
It was not clear how many protesters were detained, though footage showed at least one young man being placed into the back of a police van.
There have been consistent small protests in Brazil in the run-up to the Olympics, much of it aimed as the torch relay as it circled the country of 200 million.
Brazil is in the midst of its deepest recession since the 1930s, employment is above 10 percent, and the local currency has tumbled in value against the dollar in the last year.