The 27-year-old forward was forced off after receiving a heavy challenge from Serbia midfielder Saša Lukić, who was shown a yellow card for the tackle.
Gakpo initially attempted to continue but was unable to play on for long. Ruben van Bommel replaced him as the Netherlands completed the victory.
The KNVB confirmed on Monday that Gakpo would take no further part in the international break.
“Gakpo is not available for the remainder of the international period,” the Dutch federation said.
“The attacker went off injured in Sunday’s away match against Serbia (1-2) and returns to his club Liverpool. No replacement will be called up for Gakpo.”
The Netherlands still have two matches remaining during the international period, travelling to Greece on Thursday before hosting Serbia at the Philips Stadion in Eindhoven on Sunday.
Gakpo’s withdrawal leaves Xavi with several options on the left wing, including Van Bommel and Noa Lang. Crysencio Summerville can also operate in the position.
Further information from Eindhoven suggests Gakpo could be facing a longer absence. Journalist Rik Elfrink of the Eindhovens Dagblad reported that the forward is expected to be sidelined for “several weeks” following the examination.
The precise recovery period will depend on the severity of the injury and his response to treatment.
Gakpo had already made a strong start to the campaign before the injury, making his early departure from international duty another concern for Liverpool.
The injury occurred after Lukić’s challenge early in the match. Gakpo remained on the pitch for several minutes before ultimately signalling that he could not continue.
Liverpool will now assess the forward after his return to the club, with the extent of the problem to determine how long he will be unavailable.
For the Netherlands, his absence leaves Xavi with fewer options during the remainder of the Nations League window.
The immediate priority for Gakpo is recovery, with Liverpool awaiting a clearer assessment of the injury before his return to club action can be established.
The KNVB has confirmed that no replacement will be called into the Netherlands squad for the remainder of the international period.