I posted this to /r/askscience and got no answers. Obviously there were ecological changes from differences in hunting and destruction of habit, but I read in 1491 that diseases swept entire communities before Europeans ever arrived there. Do we have archaeological or scientific evidence of the same thing happening to populations of other animals?
New World primates like marmosets are very susceptible to many human diseases, like measles or tuberculosis. It's likely that European settlers wiped out more than one marmoset colony inadvertently, but I can't imagine it had any effect close to that caused by habitat destruction.
It's hard to isolate any disease's impact from environmental stresses; the arrival of invasive species like pigs and earthworms, the spread of European-style agriculture, the loss of annual fire clearance over much of the prairie, the devastation of keystone species like the passenger pigeon, Rocky Mountain locust, and the bison.
The closest thing to what you might be looking for: In 1904, a fungus from China arrived in the United States and killed an estimated 4 billion chestnut trees across North America. Only a few dozen of these trees still survive in the wild.