Kuyt bicycle kick goes wrong
"He tries that manoeuvre a lot but this time it went wrong," Van Marwijk told a news conference ahead of Tuesday's Euro 2012 qualifier against Group E rivals Finland in Rotterdam.
"He pulled some ligaments in his shoulder and maybe some are torn."
The 30-year-old is likely to miss Premier League matches for Liverpool against Birmingham City, Manchester United and Sunderland as well as the Merseyside club's Europa League games against Steaua Bucharest and Kuyt's former club Utrecht.
"Dirk has damaged his shoulder at the A-C joint, which is between the collar bone and the shoulder. He is likely to be out for four weeks," Liverpool doctor Peter Brukner said on the club website.
The Liverpool player's injury means Van Marwijk will be without the forward line he fielded in the World Cup final defeat by Spain in July.
Bayern Munich winger Arjen Robben is out of the Finland game with a hamstring injury while Arsenal striker Robin van Persie is sidelined by an ankle problem.
"Now the strikers are out, the others can show what they can do," said the coach.
The Dutch are also without defender Khalid Boulahrouz because of a groin injury but John Heitinga is ready to return after suspension.