Alexander-Arnold had to be replaced in the 63rd minute against City after suffering the injury and receiving medical treatment.
The 22-year-old, whose form has dropped by his standards this season, will miss England’s upcoming friendly with Republic of Ireland, followed by UEFA Nations League matches against Belgium and Iceland.
Liverpool boss Jurgen Klopp said: “Trent will be out for England, that is clear. What he has, we don’t know, but he cannot play for England.
“He will not be the last and not the only one who Gareth (Southgate) will miss for this international break. He will have a scan tomorrow and then we will see.”
Klopp bemoaned the hectic Premier League schedule for causing Alexander-Arnold’s injury, with the Reds playing in the UEFA Champions League on Wednesday night away to Atalanta, before facing City on Sunday.
Liverpool, like all Premier League teams competing in Europe this season, have practically played in midweek and the weekend of each week for the past month.
The Nations League will return this weekend, with international friendlies occurring in midweek, including England hosting the Irish at Wembley on Thursday.
In other midweek friendlies, world champions France will play Finland, world number one Belgium host Switzerland and the Netherlands entertain Spain, all on Wednesday.
Qualification for next year’s European Championships will also be up for grabs on Thursday, with match-ups between Hungary-Iceland, Northern Ireland-Slovakia, Serbia-Scotland and Georgia-North Macedonia.