The German shepherd, which belonged to Cleveland Police, was being exercised near to Ormseby Stables in Eston when it bit a 28-year-old man.
The man suffered puncture wounds on his arm and upper body and was taken to hospital. The dog handler also suffered an injury to his arm.
The force has apologised and referred itself to the Independent Police Complaints Commission.
A police spokesman said: "Based on an assessment of the animal it has been put to sleep.
"This was not an easy decision for any of the people involved, but has been made in the best interests of all those involved."
The incident occurred on 6 June.
Temporary Assistant Chief Constable Ciaron Irvine said it would be "wrong to speculate" until the full circumstances were known.
"What is clear is that this incident should not have happened and we must absolutely understand what went wrong," he added.
A police dog has been put down after biting a member of the public.