I can only speak for TNG, but in all of the missions to uncontacted worlds, no new civilizations have ever gotten sick. When the Europeans made first contact the Native Americans, the Native Americans were ravaged with myriad Europian plagues.
Does any episode/book in the Star Trek universe discuss how this is handled during first contact? Especially given the episode Journey's End it seems like European-Native relations were on the writers' minds, so I'm curious if any sort of preventative measure was ever mentioned.