More than 100 demonstrators attended the protest on Wednesday in a road near where Michael Brown, 18, was shot and killed by Ferguson Officer Darren Wilson on August 9, St. Louis County Police spokesman Brian Schellman said.
Brown's death sparked weeks of street protests and a national examination of race relations and police treatment of blacks.
Ferguson authorities say that Brown was shot after an altercation with the officer. However, witnesses say the black teenager was non-violent and compliant at the time of the shooting, and a victim of racism.
The afternoon demonstration was generally peaceful, but a number of protesters hurled glass bottles, rocks and bricks at police, Schellman was quoted by Reuters as saying.
Four people were arrested on charges they assaulted police officers, and 32 faced charges of unlawful assembly. One person was charged with both, Schellman said. Officers received minor injuries, he said.
Police closed the highway on-ramp to traffic and told demonstrators not to enter the highway, Missouri Department of Public Safety spokesman Mike O'Connell said.
Protest organizers have said that the protests involved Missouri Governor Jay Nixon's refusal to replace the St. Louis County prosecutor investigating the fatal shooting.
The protests came after Ferguson city leaders confronted demands for reform from an angry crowd on Tuesday night at their first public meeting since Brown's death.