Gallery staff chased the robber, who was described as looking like an "art student", but he threatened them with the gun.
Art experts believe the painting, named Tete De Femme, an impressionistic portrait painted in 1939 by Pablo Picasso of his then mistress Dora Maar, may have been stolen to order. But it is probably unsaleable.
The raid took place at about 11am when the man, who made no effort to hide his face and was captured on the shop's surveillance camera, strolled into the Lefevre Galley, Bruton Street.
Jacquie Cartwright, a sales assistant, said: "He looked like an art student with long hair in a pony-tail. He asked the price of the painting and I answered him.
"Then he told me he had a shotgun and he wanted the picture.
"I said 'I beg your pardon'.
"He said 'Get it off the wall for me', and I said I couldn't. I told him to get it himself, so he did and then he ran out."
Members of staff followed the fleeing man who had a taxi waiting nearby. The thief pointed his shotgun out of the cab window before ordering the unwitting driver to take him to Wimbledon in south-west London.
The taxi driver, who was left a pounds 10 tip and the picture frame on the back seat, contacted the police after dropping off his passenger.
Martin Summers, the managing director of the gallery, said the gunman took only 35 seconds to carry out the raid. "It didn't seem that he took the picture at random," he said.
The oil painting is 60cm by 45cm large and had been insured for $1m. The insurers have offered pounds 50,000 reward. It had been recently bought by the gallery. Previously it had been owned by the Picasso family collection.
Mark Dalrymple, the loss adjuster, said the painting was "impossible" to sell on the open market because it was so well known.
The owner of a nearby art gallery, Roy Miles, suggested that it may have been stolen to order.
"Obviously, a private buyer wanted a Picasso and will now hide it away and enjoy it privately, unless the police find him," he said.Reuse content