Frimpong suffered the setback during the Premier League champions' 4-2 opening win over Bournemouth at Anfield last Friday.
The former Bayer Leverkusen full-back, a reported £29.5 million ($39.6 million) replacement for Trent Alexander-Arnold, went off after an hour of his home league debut for Liverpool.
"The medical team were completely right about Jeremie to tell me to take him off because he is out until the end of the international break (September 10), and that happened during the game," Slot told a pre-match press conference ahead of Liverpool's game against Newcastle on Monday.
"I think I got criticised for taking him off, didn't I?," the Dutch boss added. "It had nothing to do with how he played, but we felt he had an issue with his hamstring and by we, I mean the medical staff. We expect to have him back after the international break."