The incident occurred shortly after Fode Ballo-Toure had put Marcelo Bielsa's side ahead in the 15th minute with fans rushing down to the front of their section to celebrate with the visiting players.
Both teams were sent to the changing rooms as the match was halted initially before a French league official later said the game had been called off.
Lille now sit third from bottom in Ligue 1 and have not won since the opening weekend of the season, where they defeated Claudio Ranieri's Nantes.
Director general Marc Ingla tweeted: "We are thinking first and foremost of our supporters".
"The club has the right to ask questions about the security arrangements and conditions imposed on our supporters at Amiens' stadium". "And so that this never happens again".
"Police warned us that 200 very angry ultras were in the section reserved for Lille fans", Joannin said (via Sportskeeda.com).
Amiens public prosecutor Alexandre de Bosschere said an investigation had been opened into accidental injury, focusing on why the barrier gave way.
Amiens later released a statement saying Joanni and some of the region's main politicians went to the Centre Hospitalier d'Amiens, where the fans were being treated.