Some of them were equipped with a machete and a hammer, police said, which they used to smash cabinets during the raid at about 7.18pm on Monday.
Officers said they made off with a “high value of goods” from Mappin & Webb.
Police said one moped was abandoned at the scene and a second bike was involved in a collision in Oxford Street.
The suspects who crashed were then picked up by a third moped – with all six reportedly fleeing on the same vehicle.
There have been no arrests.
Witnesses posted pictures on social media of the shop filled with smoke after the incident.
“Smash and grab at Regent Street jewellers. All three emergency services on scene, smoke deployed in the store,” one person tweeted.
The incident comes amid a surge in moped-enabled crime and motorcycle theft in the capital, with police often instructed not to pursue suspects for fear of the consequences if there is a crash.