The shooting happened Thursday afternoon. A witness saw the alleged shooter's car and Lansdowne police spotted the vehicle and gave chase.
Officers say the suspect lost control and crashed into a building. Upper Darby Police Superintendent Michael Chitwood says the man then put one child under each arm and took off running.
Police chased him down and arrested him.
KYW-TV reports the kids are the suspect's 2-year-old daughter and 3-year-old son. They weren't hurt.
Investigators say the shooting victim is hospitalized with non-life-threatening injuries.
The altercation reportedly stemmed from a previous argument between the victim and suspect.