Masked men robbed Kim Kardashian at gunpoint early this morning, leaving her tied up in the bathroom of her luxury residence in Paris and stealing millions of dollars' worth of jewellery, police and her publicist said.

Five attackers, wearing ski masks and clothes with police marking, struck around 3 a.m. inside the exclusive apartment block where the reality TV star was staying while attending Paris Fashion Week, a police source told Reuters.

They stole a box with 5-6 million euros' worth of jewels and a ring worth about 4 million euros, the source said.

The residence where the hold-up took place,

After she was discovered - "badly shaken but physically unharmed," according to her publicist - and news of her ordeal spread, Kardashian's husband, rapper Kanye West, abruptly ended a performance in New York less than an hour into his set.

"I'm sorry I have a family emergency, I have to stop the show," West told the audience in video tweeted by fans at the Meadows Festival in Queens. 

The robbery set social media alight, with many users expressing disbelief at the latest headline-grabbing event in the life of a TV star whose every living moment seems to be documented on screen and the internet.

"Looking forward to accompanying album and TV show detailing event," said Twitter user Jay.

Most comments, however, were supportive.

"Kim Kardashian is a mother, a wife, daughter and sister. Despite the fact that you don't like her, being held up at gun point is not funny," said one post by Alieuisha.

The armed robbery could add to worries about safety in Paris, hit by a series of attacks by Islamist militants last year.

Tourist numbers to what is traditionally the most visited city in the world, fell 6.4 percent in the first half of 2016 as many Asians and Americans stayed away.

"We worry about the image of Paris. This will be all over the news channels, imagine the negative publicity," Nathalie Kosciusko-Morizet, head of the conservative opposition in Paris, told Europe 1 radio.