The animal, described as a pit bull-type breed, was dragging the man around by his hand on Cherry Street in Blackburn late on Saturday.
The 46-year-old man suffered severe injuries to his hand and has undergone surgery at the Royal Preston Hospital.
Police said the dog was "very aggressive" and was shot by an armed officer on a grass bank.
Officers received several calls from residents about the attack, which happened just after 2300 GMT.
Roaming the streets
When police teams arrived, including an armed response unit and dog handler, the man had managed to free himself and was being treated by ambulance crews.
Insp Simon Atkinson, of Lancashire Police, said: "The animal was still roaming the streets, displaying some very aggressive behaviour to everybody in the vicinity.
"We gave every consideration to dealing with the dog as humanely as possible.
"We couldn't contain it at that time and the situation was deemed so serious, we had to take immediate action."
Insp Atkinson said the injured man was in possession of the dog, but inquiries are continuing into its ownership. It is not yet clear what breed of dog it was.
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