The 30-year-old picked up the injury during the match on Saturday’s 3-0 victory over Crystal Palace and the Reds will examine scans to discover the extent of the damage.
Liverpool visit Norwich City in the Carabao Cup on Tuesday before a league trip to Brentford on Saturday.
“I can’t say now how long it will take but not Tuesday and not the weekend,” said Reds assistant Pep Lijnders.
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“Let’s get the scan results back and we have a proper diagnosis.
“A shame as well because he was taking the game against Palace by the hand, he was a proper playmaker in my opinion. A shame that we miss him.”
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Thiago was replaced by Naby Keita after 62 minutes in the win over the Eagles at Anfield.
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Liverpool defender Trent Alexander-Arnold also missed the game against Palace through illness and will again be absent at Norwich, while forward Roberto Firmino has resumed training after missing three matches with a hamstring injury.