That doesn't make you ineligible. Ted Cruz was born in Canada but could and did run to be a presidential candidate. The rule is:
Be a natural-born citizen of the United States
That could mean that one or both of your parents are US citizens giving you a US citizenship at birth. It's just one more reason the whole Obama birther thing was nonsense, his mom is a US citizen so it wouldn't matter where he was born.
That said, Elon also does not meet that requirement.