Police said he was armed with a stolen gun and they had been tracking him. They blamed the violence on a small group of people.
Four officers have been placed on administrative leave.
The wounded man's name and age have not been released by police.
But the St Louis Post-Dispatch identified him as 18-year-old Tyrone Harris, having spoken to his father, the paper said.
The shooting of 18-year-old Michael Brown in Ferguson by white police officer Darren Wilson in August 2014 sparked demonstrations across the United States.
Although Mr Wilson was cleared of wrongdoing by a grand jury and by the US Department of Justice, the teenager's death fuelled a national protest movement against the use of excessive force by police officers.
A justice department investigation also found widespread racial bias in the Ferguson police force.
What happened in Ferguson in 2014?
US Dept of Justice report on Ferguson racism
Earlier on Sunday, hundreds of people stood silent for four-and-a-half minutes at the spot where Michael Brown was killed, representing the number of hours that his body lay in the street unattended.
The BBC's Aleem Maqbool, who is in Ferguson, says most people at Sunday's gathering felt little had changed since Michael Brown was shot dead a year ago.
At the end of a sombre, peaceful day of commemorations, shots were heard at about 23:15 local time on Sunday (04:15 Monday GMT) as a large crowd gathered on West Florissant Avenue,
St Louis County Police Chief Jon Belmar told reporters that after "an exchange of gunfire between two groups" the suspect, believed by police to be armed, left and encountered officers in an unmarked SUV.
He said the suspect fired on the vehicle and the plainclothes detectives returned fire from inside the van. There was then a further exchange of fire after the officers left the vehicle.
The gunmen "were criminals; they weren't protesters," he said, adding that the officers were not wearing body cameras.
Photos from the scene showed a young black man lying bloodied on the ground. He was face down and handcuffed.
President Barack Obama announced a federal programme to help pay for lapel-mounted cameras for US police to record their interactions in the wake of the nationwide protests on perceived policing injustices.
There have been a number of high profile shootings of unarmed black men in US cities in recent months.
The most recent case involved 19-year-old Christian Taylor who was shot dead by a white police officer after he was spotted on surveillance footage vandalising cars in Arlington, Texas, on Friday.
A man has been critically injured in Ferguson, Missouri, in an exchange of gunfire with police at a rally marking the anniversary of the killing of unarmed black teenager Michael Brown.