We report observations of the v = 1-0 S(1) line of molecular hydrogen in the high excitation Planetary Nebula NGC 2440. The emission is particularly strong at the positions of the two bright condensations which lie well within the H II region and close to the position of the very hot T = 350,000 K central star. The emission is consistent with an excited molecular hydrogen mass of 2–4 × 10−5 M⊙ in the condensations, and we estimate the total mass of excited molecular hydrogen associated with the H II region to be 6 × 10−3 M⊙. We show that the radiation pressure from the central star is insufficient to excite the S(1) line emission. We also show that a stellar wind driven shock would imply a mass loss rate of 3 × 10−7 M⊙ yr−1 if we adopt a wind velocity of 2000 km s−1.