The midfielder is expected to be ruled out for the first part of the 2023/24 season.
He has flown home from Tour to the UK where further assessment of his injury will take place before a medical decision on the next steps.
Kobbie was handed his fourth start in pre-season against Real Madrid when Brazilian forward Rodrygo landed on his leg following a tackle from United midfielder Casemiro.
The Academy graduate was forced to withdraw from the match.
The 18-year-old posted on his Instagram account following the incident.
"I’ll be back stronger and in no time," he wrote.