At about 4:20 p.m., officers responded to reports of two boxer-type dogs that were threatening a smaller dog and a child in Laurie Meadows Park.
Arriving officers said a group of adults had positioned themselves between the loose dogs and children playing soccer in another section of the park.
Some officers cleared people out of the park while others cornered the dogs, which continued to act out of control, police said.
A recorded phone alert was sent out to residents near the park advising them of loose vicious animals in the area.
Before animal control workers arrived, an officer tried to subdue one of the dogs with a Taser, police said.
The animal was not subdued and police shot both dogs, killing one and wounding the other, police said.
No people were injured in the incident.
Police are working with the Peninsula Humane Society to contact the dogs' owners regarding accountability for the incident.