Aldridge was pushing her infant child in a stroller just around the corner from the Dulles School of Excellence, a turnaround school, when several men started shooting.
One of the bullets hit her in the head. Another struck her in an arm. She died about 45 minutes later at a hospital.
The child, only about three weeks old, was unhurt, family spokesman Edward Jones said.
Aldridge's cousin, Dwyane Wade, the 12-time NBA All-Star who recently signed a contract with his hometown Chicago Bulls, employed the hashtag #EnoughIsEnough" in tweeting about her death.
"My cousin was killed today in Chicago," Wade wrote in one. "Another act of senseless gun violence. 4 kids lost their mom for NO REASON. Unreal. #EnoughIsEnough."
"These young kids are screaming for help!!! #EnoughIsEnough," he wrote in another on Saturday.
Another said: "The city of Chicago is hurting. We need more help& more hands on deck. Not for me and my family but for the future of our world. The YOUTH!"
Wade, a three-time NBA champion, was raised in Chicago and signed with the Bulls this offseason after spending 13 years with the Miami Heat.
Wade speaks out on violence
Wade has been an outspoken critic of rampant gun violence and took the stage at this year's ESPY Awards with fellow NBA superstars LeBron James, Carmelo Anthony and Chris Paul to speak about the issue.
He and his mother, Jolinda Wade, a Chicago pastor, also participated this week in an ESPN discussion on gun violence in America that was recorded at a YMCA in Chicago.
"Just sat up on a panel yesterday ... talking about the violence that's going on within our city of Chicago, never knowing that the next day we would be the ones that would be actually living and experiencing it," Jolinda Wade said, according to CNN affiliate WLS.
Wade held her crying sister Diane -- Aldridge's mother -- as she spoke with media, telling reporters this was Diane's second child who had been shot and killed.
Dispute led to shooting, police say
Chicago police spokesman Anthony Guglielmi said the shooting followed a dispute.
"We know this incident stems from some kind of encounter with an Uber driver," he said.
Three people were being questioned Saturday, he said. They all have had prior contact with police, he added.
According to the Chicago Tribune, which chronicles every homicide in the city, at least 455 people have been shot to death in Chicago in the first seven and a half months of the year.
Tuesday, Illinois Gov. Bruce Rauner signed a gun law
to combat the sale of firearms in Chicago.
The law imposes a stiff penalty on anyone without a gun-owner identification card who brings a gun into the state of Illinois to sell.
The law is meant to cut down on straw purchasers who buy guns in states with loose laws and drive them into cities with tough gun control laws.