Mourners outside the funeral home in the Gresham area were fired on from a passing vehicle, First Deputy Superintendent Eric Carter said.
Several targets of the shooting returned fire, and the vehicle later crashed and the occupants fled in several directions, Mr Carter said.
All the victims were adults, he added.
A person of interest was being questioned but no arrests had been made, according to police.
The person being questioned was uninjured and investigators have not determined how many people were involved in the shooting.
A squad car was assigned to monitor the funeral as a precaution because of the sizeable number of mourners attending, Mr Carter said, adding that he was unaware of any warnings from community activists that trouble at the funeral was imminent.
“The district commander took every precaution that he could,” he added.
Most of the victims were taken by the Chicago Fire Department to nearby hospitals in serious condition.
They include 10 women aged between 21-65, one of whom was shot in the chest.
Other victims include a man who was shot in the chest, arm and forearm, and two men aged 32 and 22, who were shot in a hand.
Police said the shooting happened at or near the site of a funeral or post-funeral event for a man fatally shot last week in the Englewood area.
“When a person picks up a gun, we suffer as a city,” tweeted Chicago mayor Lori Lightfoot. “This cannot be who we are.
Far too many have suffered. Far too many have attended funerals and tried to start the process of healing entire communities following another senseless tragedy. When a person picks up a gun, we suffer as a city. This cannot be who we are.
Advertisement— Mayor Lori E. Lightfoot (@chicagosmayor) July 22, 2020
“Too many guns are on our streets and in the hands of people who should never possess them. These individuals will be held accountable.”
The shooting comes as the Department of Homeland Security is planning to deploy dozens of federal agents to Chicago to deal with an increase in violent crime in the city.
Ms Lightfoot, after threatening to sue if President Donald Trump acted without her permission, also noted earlier that the city would be working with federal agents to fight crime.
The mayor has been sceptical of federal agents being sent to Chicago by Mr Trump due to the controversy in Portland, Oregon, where the Trump administration sent federal officers after weeks of protests there over police brutality and racial injustice that followed the death of George Floyd in Minneapolis.
Ms Lightfoot said she expects Chicago will receive resources that will plug into existing federal agencies that already work with the city, including the FBI, Drug Enforcement Agency and the Bureau of Alcohol, Tobacco, Firearms and Explosives.
