Gakpo signalled that he needed to be substituted in the 17th minute after appearing to be affected by two strong challenges in quick succession.
The 27-year-old had been in excellent form for both club and country and had scored in the Netherlands' previous match, a 1-1 draw against Germany on Thursday.
His latest injury therefore threatens to interrupt a productive start to the season.
The situation is particularly concerning for Liverpool because Gakpo's departure came only hours after Alexander Isak was ruled out of the remainder of Sweden's international fixtures with a thigh problem.
Isak has already returned to Liverpool for further assessment after leaving Sweden's camp.
Sweden manager Graham Potter described the striker's problem as minor but confirmed that the congested international schedule meant he would not be able to play.
“He's got a small problem with his thigh,” Potter said.
“It's not a big one but because of the amount of games we've got in a small space of time, he won't be able to make those.”
Potter explained that the nature of Isak's injury only became clearer after the match.
“It was during the game. Like anything, you sometimes get bumps and bruises in the game, you might think it's a bit of a dead leg or something,” he said.
“But actually as the 24 hours, 48 hours after the game, not quite what you think.”
Isak will therefore miss Sweden's remaining three matches during the international break.
Liverpool's medical staff will assess him after his return to the club, although the Premier League side do not play again until October 11, when they face Manchester City.
The Netherlands now face a similar wait for clarity regarding Gakpo.
The forward had started the international break in strong form, and he and Isak had already combined for four Liverpool goals this season.
Gakpo's latest international appearance lasted only 17 minutes before he requested to come off.
Netherlands manager Xavi Hernandez was expected to provide an assessment following the match.
For Liverpool, the timing creates an unwelcome selection concern.
The club had hoped to return from the international break with their attacking options intact, but Isak is already unavailable for Sweden and Gakpo now faces assessment after his early departure in Belgrade.
The severity of Gakpo's injury has yet to be established.
Liverpool will therefore await further medical information before knowing whether either forward will be available when club football resumes.