The shooting happened around 1:10am last Saturday during a birthday party at a small apartment complex in the 3000 block of Truxillo near Ennis.
Walter Hinton, 38 was arrested Wednesday on a murder charge, police say. He was caught at a home in northeast Houston.
Police say Hinton was bitten on the leg, allegedly by a dog owned by 60-year-old Robert Jones, and the men began to argue. Police say Hinton left the party, but returned with a pistol and fatally shot Jones, plus two other men.
Jones was struck in the abdomen and died at the scene.
Investigators say the wounded men were treated for non-life threatening injuries.
Information from the Associated Press was used in this story.