Matip was taken to hospital following the fixture and further assessment deemed an operation is required.
And Liverpool have now confirmed Matip, 27, will need surgery to fix the bone and will be out of action for several weeks.
Joel Matip was also involved in a collision in the final seconds of the game, while James Milner was forced from the pitch with cramp; however, Klopp is confident neither player has a serious issue.
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As well as missing Sunday's Premier League encounter with Manchester United, the Cameroon global will be forced to sit out of his side's meetings with Arsenal and Manchester City.
Adding to Jurgen Klopp's defensive woes, Trent Alexander-Arnold also came off in Tuesday's win over Napoli, which secured their place in the knockout phases of the Champions League, due to a foot problem.
"Millie had cramps - I hope it was only cramp", he said.
With Joe Gomez out with a fractured leg, Alexander-Arnold is the first choice right-back so Klopp will be praying he's available to face Man Utd while Matip has started the last three matches alongside Virgil van Dijk in the middle of defence.