The Manchester United striker, 22, was brought off in the 82nd minute during the Red Devils' 2-2 draw with Tottenham Hotspur, having only come on as a substitute 24 minutes earlier.
Now, BBC Sport has reported the knee injury will only keep him out for a few weeks, and it's not thought to be a major issue.
Sesko didn't take part in Slovenia's recent World Cup qualifiers, but he's set to return next month.
He has scored two goals in 12 games since joining United over summer from RB Leipzig, joining a fresh attacking lineup alongside Bryan Mbeumo and Matheus Cunha.
He could miss five Premier League games, if he's out for a month, and could return just in time for Mbeumo and Amad Diallo to join Cameroon and Ivory Coast for the Africa Cup of Nations.
The tournament gets underway in Morocco on December 21, with United playing Bournemouth at Old Trafford six days earlier.
It's not expected that United - and other Premier League clubs - will have to release players at the earliest available opportunity.
Joshua Zirkee is one option for United, while head coach Ruben Amorim could also turn to youngster Chido Obi.
Meanwhile, Kobbie Mainoo has been waiting for a chance to prove himself this campaign, and he could get his chance in Mbeumo and Amad's absence.
Amorim is set to talk to the media in a press conference before Monday's (24.11.25) home game against Everton.