The silence began at 12.02pm, the time Mr Brown was killed, with the length of time symbolising the four and a half hours that the teenager’s body lay in the street after he was killed.
Two doves were released at the end of the commemoration.
A march was also held at the site where Mr Brown, who was black and unarmed, was fatally shot by Ferguson officer Darren Wilson on August 9 2014.
His family say that they are still mourning his death.
The shooting of the 18-year-old in the St Louis suburb of Ferguson sparked nationwide protest and sometimes violent clashes between protesters and police.
The shooting helped spur what is now called the “Black Lives Matter” movement that raised questions about law enforcement, treatment of minorities and police use of military-grade equipment while controlling crowds.
In Ferguson, the teenager’s father, Michael Brown Sr, led a march that started at the memorial on the site where the youngster was shot. Time has not healed his wounds, he said before the procession, in which several hundred people, a drum corps and some cars joined in on the five-mile route.
“At the end of the day, I still lost my boy,” he said. “I’m still hurting. My family’s still hurting.”
Mr Brown said the anniversary brings back all of the grief and raw emotions, but that it is important to continue standing up to concerns about police brutality and the use of force.
As the parade began, he took an armful of stuffed toys and placed them in the middle of the street where his son died.
He said said a lot of families in the St Louis area and across the US are hurting because they have lost loved ones to police violence.
Though some groups are pledging civil disobedience in the St Louis region, Mr Brown urged everyone to mark his son’s death in peace. “No drama,” he said. “No stupidity, so we can just have some kind of peace.”
The US justice department and a St Louis County grand jury cleared Mr Wilson, who resigned in November, of wrong-doing. A separate justice department investigation of Ferguson’s justice system found evidence of a profit-driven court system and racial bias by police.
The protests picked up after dark as around 200 marchers, some riding atop cars, converged outside Ferguson’s police headquarters.
Earlier in the day, onlookers were mostly scattered in small clusters.
Ferguson interim Police Chief Andre Anderson stood alongside St Louis County Police Chief Jon Belmar and Captain Ron Johnson of the Missouri State Highway Patrol on West Florissant Avenue, waving to participants in the afternoon parade and shaking hands with some.
The street was the site of protests, looting and riots in the aftermath of Mr Brown’s death.
Police presence was limited mostly to officers keeping traffic away and there were no immediate reports of confrontations.