"As they tried to get away, police officers arrived, and three of the robbers were pulled to the ground and then arrested.
"Two others got out the back door of the hotel, and were seen running away, and then getting on mopeds."
It was at around 6.30pm that guests drinking in the Hemingway Bar, at the back of the hotel, first heard the commotion.
"Bar staff told everybody to remain calm, and not to do anything stupid. Some clients were ushered down into the basement for safety. Shots from what sounded like a handgun were heard at one point.
"There were initial fears that a terrorist attack was going on, but it soon became clear that it was a robbery.
"The attackers then used axes to smash open reinforced glass cases containing jewellery, while filling bags," said a source at the hotel.
"As they tried to get away, police officers arrived, and three of the robbers were pulled to the ground and then arrested.
"Two others got out the back door of the hotel, and were seen running away, and then getting on mopeds."
The source added: "Bar staff told everybody to remain calm, and not to do anything stupid. Some clients were ushered down into the basement for safety.
"Shots from what sounded like a handgun were heard at one point.
"There were initial fears that a terrorist attack was going on, but it soon became clear that it was a robbery."
The attackers were wearing ski balaclavas and sports clothes, and had rucksacks on their back.
The Ritz was founded by Swiss hotelier César Ritz in 1898 and has been a focus of high society ever since.
Diana, Princess of Wales, dined in the hotel's Imperial Suite shortly before her death in a car crash in August 1997.
Its retail gallery boasts several jewellers' work as well as designer goods shops.
A superior room costs from £885 a night, while a 'grand deluxe' room starts at £1240.