Kane lasted just over half an hour of the Lilywhites' eventual 4-1 win at the Vitality Stadium before heading down the tunnel in some pain.
The injury blow comes almost a year to the day since he damaged the same part of his body in an FA Cup tie with Millwall, ruling him out for a month, and he also spent time on the sidelines earlier in the 2016-17 campaign with an identical problem.
Pochettino says that it is now a case of waiting for the England international to undergo a scan on Monday before finding out the extent of his latest layoff.
"I am concerned until tomorrow, and the scan. We can say nothing more," he told Sky Sports News. "Of course I worry about him. We hope it is not a massive issue for him and the team and hope he can recover as soon as possible and be available."
Kane has netted 35 goals in all competitions for Spurs this season and was expected to play a part in England's upcoming friendlies against the Netherlands and Italy.