The 23-year-old striker missed United's 1-1 Premier League draw at Fulham on Sunday after picking up the problem in the previous week's defeat.
United confirmed on Monday that Sesko will now remain at the club during the three-week international break.
"Manchester United can confirm that Benjamin Sesko has withdrawn from the Slovenia squad ahead of the upcoming three-week international break," the club said.
"Benjamin will undergo tests this week before defining his individual recovery plan."
Sesko has scored twice for United since the start of the season but was not fit enough to feature at Craven Cottage.
His withdrawal means he will miss Slovenia's two matches against Scotland, as well as fixtures against North Macedonia and Switzerland.
Sesko is the fourth United player to pull out of international duty this week. Marcus Rashford and Kobbie Mainoo have withdrawn from England's squad, while goalkeeper Karl Darlow has left the Wales camp.
United, managed by Michael Carrick, have made a difficult start to the Premier League season and sit 12th after collecting five points from their opening five matches.
Their next league game is at home to bottom club Tottenham on October 10, giving United time to assess Sesko's injury and determine when he can return.
Norway have withdrawn Erling Haaland from Saturday's scheduled press conference ahead of Sunday's Nations League clash with Portugal in Oslo, following reports surrounding Manchester City's financial case.
Liverpool have brought Julian Ward back as sporting director, with the 45-year-old returning to the position following Richard Hughes' departure.
Italy's difficult spell continued as Belgium secured a 2-0 victory in the Nations League at the Stadio Olimpico, leaving the Azzurri facing a demanding run of fixtures.
Rodri has backed Manchester City to prove their innocence and insisted nothing can take away the success he enjoyed at the club.
