Images on social media show a person face down and apparently motionless on the ground outside Boots, with a police officer holding a gun.
Sky's home affairs correspondent Mark White said other photos appear to show him wearing something resembling a suicide vest.
Video also shows plain-clothed armed officers approaching the body on Streatham High Road, before quickly pulling back
The force tweeted: "A man has been shot by armed officers in #Streatham... The circumstances are being assessed; the incident has been declared as terrorist-related."
"We believe there are two injured victims. We await updates on their conditions," the force added.
A witness described seeing a man with a machete and silver canisters being chased before he was shot dead.
Gulled Bulhan, 19, said: "I was crossing the road when I saw a man with a machete and silver canisters on his chest being chased by what I assume was an undercover police officer - as they were in civilian clothing.
"The man was then shot. I think I heard three gun shots but I can't quite remember.
"After that I ran into the library to get to safety. From the library I saw a load of ambulances and armed police officers arrive on the scene."
Metropolitan Police have urged people to avoid the area and London Ambulance Service said they had a "number of resources" at the scene.
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