Goal scorer Henry was forced out if the Red Bulls' 1-0 win over New England with the injury.
"His injury is disastrous for us. His leadership in every single training session is invaluable. It's a huge loss for us, both on and off the pitch. It's going to be difficult now without him,'' Backe told the New York Post.
"No, it's a quite big hamstring, a huge one, so normally you say three or four weeks. I think he did quite a sprint to try and get in behind and then he stopped quick, and then he picked up the hamstring.''