What is the proper form?
send an e-mail
send a mail
First of all, it's not often that you'll find someone referring to email as "e-mail". Mostly there is no hyphen. Just a note!
To answer your question, definitely "send an email". As in:
"I'm going to send an email over to Katelyn about that."
However, while this isn't wrong, it's actually most often shortened even more, to just "email" like this:
"I'm going to email Katelyn about that."