The incident happened in Prior Street near Circus Street just before 5.10pm yesterday (March 2).
Officers attended and a man in his 40s was arrested on suspicion of offences under the Dangerous Dog Act.
He remains in police custody.
Two dogs belonging to him were seized and their breed has not been formally confirmed.
The incident is under investigation.
A Metropolitan Police spokesperson said: “Police were called to a reported dog attack in Prior Street, Blackheath at 17:09hrs on Sunday, 2 March.
“Sadly, a Jack Russell dog died at the scene.
“A man in his 40s was arrested under the Dangerous Dog Act and taken into police custody where he remains. Two dogs in his possession were also seized.
“The breed of the two dogs is yet to be formally confirmed. This incident is still under investigation.”
