He was performing as part of the Lucha Libre Mexican wrestling show at the Roundhouse last night.
A large audience was reportedly cleared from the venue after Barrón suffered a fall which left him unconscious in the ring.
Confusion ensued, with fellow wrestlers realising there was a problem when he did not respond to the referee's calls for him to get up.
According to the Camden New Journal, he was turned over and counted out, but when he still did not get up after that, organisers and a team of medics rushed onto the stage.
The report says fans chanted ‘Silver, Silver’, still believing it was part of the show, before realising the seriousness of the incident.
After being told there would be a break in the show, the audience were shortly afterwards cleared from the venue with ambulances and police having turned up at the scene.
The Camden New Journal quoted one audience member saying: “It seemed to be part of the show at first but then he didn’t get up – and then the medical team was on the stage.
"Everybody was cleared out and lots of police and ambulances were there.”
A tweet from the Roundhouse confirmed there had been 'an incident' but did not go into detail.
The tweet read: "There has been an incident at the Lucha Libre show at the Roundhouse this evening.
"At this time we are unable to share further information."
As well as WCW, Barrón performed in the Universal Wrestling Association, Consejo Mundial de Lucha Libre, All Japan Pro Wrestling, New Japan Pro Wrestling (NJPW) and various smaller federations all over the world.
Barrón played the villain Ramses opposite Jack Black's character Nacho in 2006 film Nacho Libre.
The film is based on the story of a real-life Mexican Catholic priest who had a 23-year career as a masked wrestler.
A statement from WWE said: "WWE is saddened to learn that Lucha Libre legend and former WCW star Silver King has passed away at age 51.
"A champion luchador in his native Mexico, Silver King, real name César Cuauhtémoc González Barrón, entertained audiences across the globe, and was a standout in WCW’s Cruiserweight division in the late ’90s. Outside the ring, he appeared under a mask as the villainous Ramses in the popular 2006 comedy “Nacho Libre.”
"WWE extends its deepest condolences to Silver King’s family, friends and fans."