These cameras have enhanced sensitivity to red and "far red" because of the filter used on the sensor. Tiffen makes a T1 IR filter for this reason. Usually it's manifested in "brown" blacks in certain circumstances, such as many black synthetic fabrics. I've often suspected that my camera's tendency to auto-balance a bit "cool" was due to this.
I haven't sat down and done a comparison with/without the filter on, but I suspect this may help in such a case.
The same thing happened to me once or twice with my original EX1 which at the time was one of the first batch of cameras sold. I remember turning on the camera and the view screen showed a green picture just like yours. I think the problem was software, in that sometimes the camera didn't boot up properly. Once Sony did a firmware update I never saw that problem again and it's never appeared on my EX1R or EX3.
If you shut your camera off and the problem goes away after you start up I would just be aware that this will happen from time to time. If the problem persists on a regular basis then try this: if you have picture profile settings on your camera and want to keep them, transfer them to one of your SxS cards and then utilize the "RESET ALL" in the OTHERS menu.
If that doesn't work then get your camera to Sony for a checkup and a firmware update.