The tool I would try first is the spot healing brush tool (I believe CS5 and later). It's at the top of the list of healing tools if you press the shortcut key "J". Click on one end of the white line, then holding shift click on the other end. The Shift+click will draw a straight line across. The line isn't exactly straight so you may have to use a slightly wider brush. This may not give perfect results, but should do a good job and you can then clean up with clone stamp or other tools. If you do it in a duplicate layer you can mask out any areas that you don't like and try a second swipe.

After that, duplicate the image and add a black mask to hide it. Use the move tool to move the duplicate layer up and over a few pixels (the width of the line or a bit more). Then using a white brush paint over the white line to let the duplicate layer to show through revealing pixels from the green background and zebra.