He will now miss the rest of the season, ruling him out of contention for the Three Lions' opening Euro 2020 qualifiers and the inaugural Nations League Finals in June.
"AFC Bournemouth midfielder Lewis Cook will be sidelined for six-to-nine months with a ruptured anterior cruciate ligament," a club statement read.
"Cook was assessed by the club's medical staff following the match, with further assessment and scans on Wednesday revealing the extent of the damage to his right knee."
Bournemouth manager Eddie Howe said: "We are all devastated for Lewis. It is a huge blow to a very talented player who has been a very important part of our side over the last 18 months.
"But Lewis is a strong character who only has to look around our dressing room for inspiration of how an injury like this is merely a setback and to know that he can come back better than ever.
"He will have the full support and love of everyone at the club throughout the next few months as he receives the very best treatment and rehabilitation possible."
Bournemouth, who are back in action at home to title chasing Liverpool on Saturday, have had to deal with a succession of knee injuries to first-team players since promotion to the Premier League in 2015.
Defender Adam Smith will be sidelined into the new year with a cartilage tear, while top scorer Callum Wilson has twice sustained similar setbacks to the one Cook must endure.
Tyrone Mings missed the vast majority of the 2015-16 campaign after suffering torn knee ligaments 12 minutes into his debut against Leicester City.
Aside from Liverpool, the Cherries are to face both Tottenham and Manchester United before the end of December and will also take on Chelsea in their Carabao Cup quarter-final at Stamford Bridge.