Police say 26-year-old Demarcus Lyons barricaded himself inside the house with the woman and his two young kids.
When officers arrived at the home, Lyons opened a window and fired a shotgun at them.
After a short stand-off, Lyons ran out of the house and tried to escape from police before being wrestled down and arrested.
The suspect's girlfriend and children were not injured in the stand-off.