The 26-year-old was forced to come off in the first half of that 2-0 victory, which sent Arne Slot's side five points clear of reigning champions Manchester City at the top of the rankings.
Barely a couple of minutes after Darwin Nunez had given Liverpool the lead, Alexander-Arnold was seen sitting on the turf with an apparent problem and immediately made way for Conor Bradley.
Slot did not have any positive updates to give on Alexander-Arnold's fitness in his post-game press conference, admitting that the defender having to make way early was not a good sign.
However, the early indications were that Alexander-Arnold had not picked up a serious problem, and according to journalist Paul Joyce, he is only expected to be sidelined for a couple of weeks.
How many games will Alexander-Arnold miss?
While the news is good from a Liverpool sense, it is a major blow for England interim boss Lee Carsley, who had called Alexander-Arnold up to his squad for this month's UEFA Nations League matches with Greece and the Republic of Ireland.
However, the Liverpool academy graduate is now certain to withdraw from the squad for November's fixtures, and an official announcement from the Three Lions is likely to arrive in due course.
As things stand, Alexander-Arnold is a slight doubt for Liverpool's first game back, which comes away to Southampton on November 24, but he has not been ruled out of the clash with the Saints.
In addition, there is hope that the defender will be given the green light to face Real Madrid - his reported admirers - in the Champions League on November 27, as well as Manchester City on December 1.
Joyce adds that Alexander-Arnold escaped with a minor problem thanks to his early withdrawal on Saturday evening, as trying to play through the pain could have led to a more serious problem.
Will any other injured Liverpool players return this month?
For the time being, Alexander-Arnold will take up a bed in the Liverpool infirmary with four other injury victims in Diogo Jota (abdominal), Federico Chiesa (fitness), Alisson Becker (thigh) and Harvey Elliott (foot).
There was initial hope that all of the latter four players would be fine to come back for the Southampton trip, but Slot has now conceded that Jota may not return for another two weeks after the international break.
As a result, the Portugal international may not be fit for either heavyweight clash against Real Madrid or Man City, but he should have recovered in time to face Everton in the Merseyside derby on December 7.
However, Elliott is on the verge of coming back from his long-term foot fracture, while Alisson is also recovering well, so there is a chance that the pair could be in the squad to tackle Southampton.
Slot is expected to take a much more cautious approach with Chiesa, though, as the ex-Juventus winger has been plagued by numerous injury problems in recent times, so it would not be a shock to see him held back.