Armed police were sent to The Chase in Braunstone Town, Leicester, after reports about an animal attacking another dog and its owner.
Leicestershire Police said the injured man, believed to be in his 30s, needed hospital treatment for puncture wounds to his legs while his pet needed veterinary treatment.
The dead dog is not believed to have been with its owner during the attack, a spokesman for the force added.
Nobody else was hurt during the incident which happened at about 7.05pm.
"On arrival the attacking dog continued to be aggressive and attack the dog and its owner," said Leicestershire Police.
"To prevent further injuries and possible attack, the decision was deemed necessary to deploy Taser.
"The dog subsequently died."
The police have appealed for anyone with information to contact the force on 101.