The shooting happened at Warren Park in northeast Houston at about 7:30 p.m., according to police.
HPD said the girl snuck out of the house to meet her boyfriend, who is around 17 to 18 years old.
Relatives reportedly went to find the girl and saw her at the park with the teen. That's when the teen pulled out a gun, shot one of the girl's relatives, and took off.
When authorities arrived, they found a man with a gunshot wound to his arm. The victim was transported to the hospital in serious condition, HPD said.
Police said the 14-year-old remained at the scene with her family.
No one else was reported to be injured.