Officers on the island confirmed the fossils, which are clearly visible on the coastline at Staffin, were most likely damaged sometime yesterday by an individual who had poured plaster over them.
Police are looking to speak to a male campervan driver who was seen in the area.
The footprints, the only examples of their kind in the country, were formed in the middle part of the Jurassic period, at a time when Scotland was part of a huge island landmass, partly covered by oceans with lagoons and river deltas in between.
Staffin is the only place in Scotland where dinosaur fossils have been recovered.
“What’s so exciting about them is not just that they are Scottish dinosaurs but that there are very few dinosaurs anywhere in the world from that time,” Steve Brusatte, a paleontologist at the University of Edinburgh, told The Scotsman last year.
“It’s a really dark period for understanding dinosaurs so Scotland has something cool to offer. It’s a unique window into this mysterious era.”
Skye, known as ‘dinosaur isle’ because of its rich fossil heritage, was targeted by thieves in 2011.
Looters hacked several tonnes of rock from cliffs near Bearreraig Bay in an apparent organised search for valuable fossils.