The Norwich City man scored his first international goal as the Dutch topped Group B with a 2-0 win over Chile on Monday, but sustained his knock during training the following day.
"The severity of the injury to the seven-time international's left hamstring should emerge over the next few days," read a statement on the Dutch Football Association's (KNVB) official website.
Fer was, however, able to offer some more positive news to fans of his club side by committing his future to the Carrow Road outfit, despite their recent relegation from the Premier League.
"We had a really disappointing season and getting relegated was a bad moment for everyone at the club," he said. "For myself, it’s a difficult feeling to come away with Holland and forget about what happened at Norwich. But I have had to refocus on the World Cup because this is a different situation to my club.
"Whatever happens here in Brazil, I am a Norwich player. I am contracted to them for the next three years so my commitment is to them.
"I am not thinking about anything else at the moment other than going back to Norwich for the new season."
The Netherlands face Mexico in Fortaleza on Sunday.
