It happened Thursday in the city's West Town neighborhood near Halsted and Hubbard.
Police say 50-year-old Robert Simmons got in a nearby vehicle and drove away after grabbing the purse. The woman followed in her car until Simmons crashed a few blocks away.
Witnesses helped detain Simmons until police arrived. He is charged with felony vehicular invasion.
Simmons is on parole from a six-year prison sentence for car theft.
The woman and child were not hurt, and her purse was recovered.