The 2018 French World Cup winner suffered an injury to his left thigh as Monaco trained at the English national football centre at St George's Park after beating Liverpool in a friendly on Sunday.
The 33-year-old midfielder was only returning to group training after a long spell of right-knee problems.
Pogba has played only one half of football for Monaco in this pre-season.
According to several sources close to the matter, the new injury shows Pogba is some way off the level of fitness required to begin the Ligue 1 season.
After serving 18 months of a four-year ban for doping, Pogba played just six Ligue 1 matches for Monaco last season, totalling 115 minutes on the pitch.