Police said it appeared the helicopter had hit the crane on top of a building. They said it was too early to confirm any casualties.
Police said they first received calls at 08:00 GMT and the London Ambulance Service said it was also at the scene.
Transport for London has confirmed there has been an incident.
Witnesses reported seeing debris on the ground.
Quinn Murray was cycling when he saw the crash.
He said: “I saw the helicopter hit the top of the crane and come down just to the left of the station.
“There was quite a large amount of fire and a huge smoke cloud. It wasn’t on the road, but into a building site where they are building the new Nine Elms area.
“There’s a huge number of emergency services.”
Commuter Sherna Noah described seeing a “large plume of dark grey smoke” as she crossed Battersea Bridge at about 08:00 GMT.
She said: “I was coming across the bridge and basically I could see a few cyclists on the bridge looking towards the water.
“I looked over to see what they were looking at and could see a pall of grey smoke coming from the south side.
“You could see a large plume of dark grey smoke.”
Nicky Morgan, the MP for Loughborough, witnessed the crash while walking towards Vauxhall station from the Lambeth Palace direction.
She said she heard an enormous bang and saw clouds of black smoke.
At least four ambulances and many police cars were at the scene.
Wandsworth Road near Vauxhall station is closed, with apparent debris on the ground, and a crane at the top of a new high rise development appears to be damaged.
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