Spurs beat the Italian side 2-0 at Wembley in their final fixture before the new league campaign but Trippier was withdrawn shortly before half-time.
"We hope it's not a big issue. It's his ankle," Tottenham manager Mauricio Pochettino said of the 26-year-old.
"He's better now than he was at half-time, but we must wait."
After England right-back Kyle Walker left the north London club to sign for Manchester City, Trippier had been expected to be Spurs' first-choice right-back this term.
If the former Burnley full-back is sidelined, 20-year-old Kyle Walker-Peters could be in line for his Premier League debut when Tottenham travel to Newcastle on Sunday, 13 August.
Trippier had provided the cross for Harry Kane's opening goal against the 2017 Champions League finalists, before Christian Eriksen netted the second after the break.
Tottenham right-back Kieran Trippier limped off with an ankle injury in the friendly win over Juventus just a week before the start of the Premier League.