The infrared S(1) line of molecular hydrogen has been searched for in twenty-two planetary nebulae using the imaging mode of the Anglo-Australian Telescope. The line was detected and mapped in eleven objects. It has been demonstrated that all those with strong excited molecular hydrogen belong to a subclass of the Type I planetary nebulae, morphologically consisting of an equatorial toroid with faint bipolar extensions. Furthermore, nearly all planetaries with these characteristics have strong molecular hydrogen. The molecular line ratios in the 2.0 to 2.5 micron window are consistent with shock excitation. The observations suggest that the morphology of these planetaries has been controlled by a fast stellar wind interacting with a disc of gas concentrated in the equatorial plane.