The injury to Simons comes amid Spurs fighting for Premier league survival.
Tottenham are in the relegation zone in 18th place and two points from safety with four games left.
The 2026 World Cup, which is taking place in the United States, Canada and Mexico, begins on 11 June, with the Netherlands starting their campaign in Group F against Japan on 14 June.
“All I’ve wanted to do is fight for my team and now the ability to do that has been snatched away from me … along with the World Cup,” added Simons.
“Representing my country this summer … just gone. It’ll take time to find peace with this, but I’ll continue to be the best team-mate I can be. I have no doubt that together we’ll win this fight.
“I’ll walk this path now, guided by faith, with strength, with resilience, with belief, as I count down the days to getting back out there.
“Be patient with me.”
Simons joined Tottenham from RB Leipzig for £52m last summer and has made 28 league appearances for the club this season, including 19 starts.
He has scored two goals in the top-flight and registered five assists but has struggled to make a major impact during a season in which the club have parted ways with managers Thomas Frank and Igor Tudor, who was in interim charge, before appointing Roberto de Zerbi.
Simons also joins a lengthy Spurs injury list heading into their final four Premier League games against Aston Villa, Leeds United, Chelsea and Everton.
Striker Dominic Solanke also went off injured at Wolves, while Ben Davies, Mohammed Kudus, Dejan Kulusevski, James Maddison, Wilson Odobert and Cristian Romero are all sidelined.