The Hyundai driver lost control on ice then slid off the road and into a bank, on which someone was standing.
Footage showed the spectator tumble down the bank and other spectators rush to check on the person.
Paddon and co-driver John Kennard were not injured.
"A spectator was transported by helicopter from the stage to hospital in Nice. Despite the best efforts of the medical staff, the spectator has sadly died.
"An investigation has commenced into the incident and all involved parties will provide assistance to the authorities. Everyone associated with the event extends their deepest sympathies and condolences to the families, friends and individuals affected."
Hayden Paddon RallySport Global Ltd said "this is an extremely sad end to a difficult day for Hayden and John. There will be no further comment from either of them at this time".
Following the crash the stage was cancelled by rally organisers. A second stage is set to get under way.
Conditions were treacherous in the hills, where the night-time stage was being held. Black ice featured prominently in 0 degrees C, making it difficult for drivers to judge grip levels.
Four-time world champion Sebastien Ogier and Paddon's Hyundai teammate Thierry Neuville had already completed the stage when Paddon had his crash. Both drivers spoke of difficult driving conditions.
Shortly after the crash, Paddon was seen on television coverage, frantically waving his hands. His car didn't appear too damaged and, in normal circumstances, they would have tried to get the Hyundai i20 back on its wheels to finish the stage.
It is the worst possible start to the new season for the World Rally Championship, which ushered in a new spec of cars and welcomed Citroen and Toyota back into the championship.
Monte Carlo is known as one of the more technical courses on the world rally circuit. Drivers may not be a top speed, but would still be grappling with more power through corners.
