Both prepositions are correct. A dictionary search suggests that "nervous about" is more common in the U.S. and that "nervous of" is more common in the U.K., although the two expressions show up in citations on Google from both major linguistic communities.
The Longman Advanced American Dictionary (2000) gives these example sentences for "nervous":
"” I didn't know him and was really nervous about having to work with him | Job cuts are making auto workers very nervous about the future
In contrast, the Longman Dictionary of Contemporary English (2003), which is a dictionary of mainly UK English, gives examples with both prepositions:
"” She was so nervous about her exams that she couldn't sleep ... | [+of] We were all a bit nervous of him at first
Here is an extended passage from Google that contains three different prepositions after the adjective "nervous":
"” Dental techniques have improved so much over the last few years, that modern dental treatment can now be completely painless. Despite this, most people still feel a little nervous at the thought
of going to the dentist.... As someone who is nervous about dental treatment
, you need to be looked after by a dental practice that will take special care of you – it's just a matter of finding the right one for you....There are many organisations that help people suffering from phobias. Most of them also offer help to people nervous of the dentist
because it is a very common problem....http://www.dentalhealth.org.uk/faqs/leafletdetail.php?LeafletID
This example is UK English.
One impression I get from looking at the Google examples is that "nervous of" occurs a lot with plural and mass nouns that are general, e.g. nervous of
spiders, heights, traffic, crowds, swimming, strangers, nuclear power
...when "nervous of" really means "afraid of." This impression accords with jaybel's last example, "I am nervous of exams," which sounds perfectly fine.