The closed casket of Brown, 18, adorned with two photos of him as a child and several garlands of white and red flowers, was at the centre of the ceremony at the Friendly Temple Missionary Baptist Church in St. Louis.
Hundreds of people had congregated since dawn to attend the service.
The Rev. Al Sharpton had words of comfort for the parents of the dead teenager, Michael Brown Sr. and Lesley McSpadden, and also a message for the authorities.
"We are required to leave here today and change things. Michael Brown must be remembered for more than disturbances. He must be remembered for this is when they started changing what was going on," Sharpton said.
Among those in attendance were the Rev. Jesse Jackson; Martin Luther King III, son of the slain civil rights leader; director Spike Lee and three White House officials.
Sharpton slammed the fact that the youth's body was left almost 4 1/2 hours in the street for all to see, and asked what the circumstances were "to have that boy lying there, like nobody cared about him. Like he didn't have any loved ones, like his life value didn't matter."
Following the plea by Michael Brown Sr. that this Monday be a day of peace, the reverend addressed those who had committed looting and disturbances during the days of protest after the Aug 9 shooting.
"Michael Brown does not want to be remembered for a riot. He wants to be remembered as the one that made American deal with how we gonna police in the United States," Sharpton said.
The Brown case has exposed the racial differences still underlying American society, and the economic and social inequalities that exist in some communities like Ferguson, a town where two-thirds of the roughly 21,000 residents are African American, but all three members of the police force are white.
Schools opened normally this Monday in Ferguson to begin the school year, a week late because of the disturbances but now that calm had been restored over the weekend by the NAACP march that went off peacefully.