Gakpo was forced off after just 17 minutes in Belgrade following a challenge from Serbia midfielder Sasa Lukic. The forward attempted to continue but was unable to play on and was eventually replaced by Ruben van Bommel.
The Dutch football federation confirmed that Gakpo will take no further part in the current international window and that no replacement will be called up by head coach Xavi Hernandez. He is expected to undergo further assessment by Liverpool's medical staff to determine the severity of the injury.
The 27-year-old has made a productive start to the season, registering two goals and four assists for Liverpool. He had also scored in the Netherlands' 1-1 draw with Germany in Hernandez's first match in charge.
Gakpo is now set to miss the Netherlands' upcoming Nations League fixtures against Greece and Serbia. His availability for Liverpool's next match remains uncertain, with the Reds scheduled to face Manchester City in the Premier League on October 11.
Liverpool have also seen striker Alexander Isak leave international duty with Sweden after suffering what has been described as a minor injury.
Isak completed the full 90 minutes during Sweden's 2-1 victory over Romania on Friday, but subsequently withdrew from the squad. He will miss Sweden's next three Nations League fixtures and will return to Liverpool for assessment by the club's medical team.
The injuries to Gakpo and Isak leave Liverpool monitoring two important attacking players during the international break, with further updates expected once both have been assessed at the club.
