It was followed by a tense stand-off involving police and protestors during which police fired crowd control rounds - known as beanbags - at people who had been at the funeral.
The authorities have been trying to prevent a repeat of rioting sparked by the police shooting of a black teenager.
The funeral of 19-year-old Timothy Thomas took place amid emotional scenes on Saturday.
It was followed by a tense stand-off involving police and protestors during which police fired crowd control rounds - known as beanbags - at people who had been at the funeral.
Anyone still in the streets during the curfew is likely to be arrested and charged by police, who are out in force.
A BBC correspondent says such confrontations, after the highly-charged emotions of the funeral could easily end in further violence.
The funeral looked like passing off peacefully despite bitter condemnation of police racism by preachers.
Mourners streamed past the coffin bearing Thomas's body as the service was relayed on loudspeakers to hundreds of people who could not get in to the crowded church.
While uniformed police were nowhere to be seen near the church, they were in the general area in large numbers, and helicopters could be seen hovering overhead.
Out of the blue, four police cars pulled up at a street corner as the funeral was ending and fired control rounds, seemingly unprovoked, at the crowd.
A woman was injured and the crowd headed towards lines of riot police.
Some people staged a sit-down protest, but were persuaded to give up after negotiations with a senior black police officer.
The shooting of Thomas sparked three days of riots, prompting the city's authorities to impose a curfew.
Thomas was unarmed, but running from Officer Steve Roach when he was shot.
Officer Roach has said he thought Thomas was reaching for a weapon.
Among those at the funeral were Kweisi Mfume, president of the NAACP, the Rev Martin Luther King III and Malik Zulo Shabazz of the radical New Black Panther Party.
Mr Shabazz said that the death of Thomas should serve as a "rallying point".
Correspondents say that, although the curfew seems to have deterred incidents of violence, it has not quashed black accusations of police racism.
The police officers' union has hit back at these accusations, condemning them as "inflammatory, racist and unfair".
Fifteen black men have been killed by the police in Cincinnati in recent years.