The veteran Brazil defender lasted just 19 minutes of the 2-0 defeat in North London which left Chelsea stuck in 10th position on the Premier League table.
The news presents a fresh headache for Chelsea manager Graham Potter, who is looking to arrest the club's poor form.
Chelsea have won just twice in their last 15 matches across all competitions and will be looking to overturn a 1-0 deficit to Borussia Dortmund in the Champions League round of 16 stage second leg without the 38-year-old.
"Having sustained a knee injury during the first half of Sunday's match against Tottenham Hotspur, Thiago underwent further assessment and a scan on his return to the training centre on Monday," a club statement read.
"Scan results from those assessments have confirmed damage to Thiago's knee ligaments and he will now work closely with the club's medical department during his rehabilitation to return to action as soon as possible."
Silva signed a one-year extension to his Chelsea contract earlier this month.
The former AC Milan defender joined Chelsea on a free transfer from Paris Saint Germain in the summer of 2020 and has helped the Blues win the UEFA Champions League, UEFA Super Cup and FIFA Club World Cup in his time at the club.
