The setback leaves the Premier League champions facing a demanding run of fixtures without one of their most important players.
Alisson was forced off in Istanbul and underwent scans on Thursday, which revealed damage expected to keep him sidelined for around six weeks. That absence could see the Brazilian miss up to eight matches, stretching beyond the November international break.
Speaking at his press conference ahead of Saturday's clash with Chelsea, Slot admitted his number one would not be available. "Alisson is not part of the squad tomorrow and he's not going to travel to Brazil for the national team.
"He will be out for Saturday (against Chelsea)," the Liverpool manager said.
Pressed on a potential return date, Slot added: "That depends on how fast a recovery goes. It's clear he's not here Saturday, not going to play for Brazil, and I would be surprised if he would be there for the first game after the international break."
The 32-year-old has endured a history of muscular problems, and Slot acknowledged concerns but refused to speculate further. "I'm not a doctor, so I cannot tell you if it's the same every time.
"What I'm mainly interested in is if he can play at the weekend and how long it will take," he said.
Giorgi Mamardashvili will step in against Chelsea, with Freddie Woodman taking a place on the bench.
There was brighter news regarding Hugo Ekitike, who was also withdrawn against Galatasaray. Slot confirmed the French forward has returned to training. "Hugo is going to train today again and let's see where he is.
"The same can be said of Federico (Chiesa). We have to wait and see after the session," he explained.
While Ekitike's involvement against Chelsea remains uncertain, his recovery is an encouraging sign as Liverpool navigate a difficult period.
With the Premier League champions stretched in key positions, Slot's ability to adapt could prove decisive in their defence of the title.
Nigeria international Samuel Chukwueze has expressed his excitement at rediscovering top form at Fulham, crediting manager Marco Silva for playing a crucial role in his resurgence.
Liverpool striker Mohamed Salah claims he feels like the club is trying to place the blame for their poor form squarely at his feet.
Leeds completed a stunning comeback from 2-0 down to snatch a 3-3 draw against a reeling Liverpool and pile fresh misery on Arne Slot.
Manchester City secured a second successive Premier League victory at home against Sunderland, Chelsea were held scoreless away to Bournemouth while Tottenham managed to beat Brentford.
