The shooting occurred in the Burnside area of Chicago around 8:20 a.m., police said.
The argument began because the two men disagreed on who should walk the family dog, Chicago Police spokesperson Anthony Guglielmi said in a tweet.
A man shot and killed his 22-year-old son in the USA after an argument between the two over who would walk the family dog escalated into a shootout. They were both rushed to Advocate Christ Medical Center.
The names of the men have not been released.
His father is now in a critical condition, the Chicago Tribune reported. The son was in serious condition when he arrived, but he was later pronounced dead, the report stated.
Police recovered two weapons from the scene. The older man, 43, was listed in critical condition. So far this year, Chicago has had 816 shooting victims.
Since Friday, six people have been killed and 22 others injured in shootings across the city, the Chicago Sun Times reported.