The 30-year old forward sustained the ruptured ligaments whilst training with Holland in preparation for their Euro2012 qualifier with Finland and Hodgson thinks it may take longer than a month to have him back in action.
"It's one of those injuries where it's very tough for the doctor to say. Four weeks is a very conservative estimate," he said.
"We have to be very careful because it's the type of injury that has to be treated with a lot of respect. It's a great blow as Dirk is an important member of our first team.
"He's a quick mender and has a great attitude towards recovery, so he will be back as quick as is humanly possible. But it's looking at least a month and possibly longer."