During the robbery, the gang of five smashed the window of a jewellery store at the hotel with axes and looted the pieces on display, Xinhua reported.
As the robbers opened fire on the hotel, guests at the Hemingway bar were told to "get down", eyewitnesses have said.
"One man wearing a ski mask ran right from the bar door to the front, right past my father".
The French TV station BFM said that €4.7m (£4.16m) worth of jewels have been taken.
Mazda to build $1.6B production facility in Alabama
A Toyota automaker employee moves an engine at the Toyota engine assembly line in Huntsville, Alabama November 13, 2009. The decision to pick Alabama is another example of foreign-based automakers building USA factories in the South.
"We heard a loud noise and lots of racket in the street", one hotel employee told AFP.
The robbers arrived at the hotel at about 6.30pm (5.30pm United Kingdom time) before smashing the windows and making off with the jewellery.
Armed heists targeting jewellery stores are not uncommon in the ultra chic avenues near Place Vendome square in central Paris where the Ritz is located.
The Ritz has played host to scores of famous people since it opened in 1898.
Serena Williams suffered from blood clots, hematoma after baby
Williams also revealed that she tries not to look at her sister Venus Williams's face when the two are playing against each other. Williams returns to tennis in March. "It's interesting", Williams is quoted as saying.
The landmark Paris Ritz hotel re-opened its palatial doors to guests in 2016 after almost four years of renovations and a major fire.
The Luftwaffe set up their regional headquarters at the Ritz during the Second World War.
It was the last place Princess Diana stayed before her fatal auto crash and is popular with elite guests from around the world.
The hotel, owned by Mohamed Al Fayed, reopened last year after four years of refurbishment work.
Iran bans English in schools amid 'cultural invasion' fears
It comes after a week of protests against the Iranian government in which 22 people have been killed and more than 1,000 arrested. Ayatollah Khamenei blamed unspecified external "enemies" for the unrest.