Alli picked up the injury in training and was missing in action as Tottenham lost to Inter Milan on penalties following a 1-1 draw in the International Champions Cup on Sunday.
Alli has suffered a number of hamstring problems in the last two seasons, and missed twelve games at the start of the year.
Tottenham begin their Premier League campaign with a home game against newly-promoted Aston Villa on Saturday, but will be without the 23-year-old.
"I don't know if the club communicate the time but I don't believe he is going to be ready for the start of the season," Pochettino said of Alli’s latest setback.
"It's the same area [of his hamstring]. Yes of course we are worried he is still so young.
"Just 23-years-old and many, many hamstring problems in the last few years. It's to pay attention to what is going on in his body but we are trying to help him.
"Think a minor injury, only a few weeks until he can be available again and be with the group."
Pochettino has only added Tanguy Ndombele to his squad ahead of the new campaign but is still looking to conclude deals for Fulham youngster Ryan Sessegnon and Real Betis midfielder Giovani Lo Celso.
Alli made 38 appearances in all competitions for Tottenham last season, scoring seven goals.
