Yes
Specifically, the dodo was a magical creature:
The Diricawl originated in Mauritius. A plump-bodied, fluffyfeathered, flightless bird, the Diricawl is remarkable for its method of escaping danger. It can vanish in a puff of feathers and reappear elsewhere (the phoenix shares this ability; see page 32).
Interestingly, Muggles were once fully aware of the existence of the Diricawl, though they knew it by the name of “dodo.” Unaware that the Diricawl could vanish at will, Muggles believe they have hunted the species to extinction. As this seems to have raised Muggle awareness of the dangers of slaying their fellow creatures indiscriminately, the International Confederation of Wizards has never deemed it appropriate that the Muggles should be made aware of the continued existence of the Diricawl.
—Fantastic Beasts and Where to Find Them
Although Muggles did not succeed in hunting it to extinction, we know from contemporaneous Muggle accounts and pictures (which presumably exist in the Potterverse as well), that Muggles did indeed succeed in recovering the bodies of some dodos, which would suggest that they did probably seriously reduce the Diricawl population. Of course, it was perhaps never at much risk of extinction, due to its powers of teleportation.
It also seems possible that Muggle activity could threaten the Firecrab,
Despite its name, the fire crab greatly resembles a large tortoise with a heavily jewelled shell. In its native Fiji, a stretch of coast has been turned into a reservation for its protection, not only against Muggles, who might be tempted by its valuable shell, but also against unscrupulous wizards, who use the shells as highly prized cauldrons.
—Fantastic Beasts and Where to Find Them
Whether this actually did happen in the past, before the adoption of the International Statute of Secrecy, is unknown.
