Identified as Han, the man was apprehended at a spa center today and has been detained for intentional homicide.
The incident happened yesterday near a bus station in Beijing's Daxing district where Han wanted to park his car.
He asked a woman standing there to move aside who refused to do so as she was attending to her baby girl at the time, state-run newspaper China Daily said.
After a preliminary investigation, police arrested Han, a 42-year-old former convict from Fangshan district.
He was released from prison earlier this year after serving his sentence on charges of theft, police said.