Change your E-Mail password, looks like some sort of spam, the only thing Malware related would be if there is an attachment to the E-Mail.

Very common that someone else somewhere has a virus infection, and has your email address on their computer either from direct communications with you or via forwarded messages from other people. Malware/viruses commonly scan through material on the infected computer and pick up addresses to fake the sender on messages they spew. The target mail server of the recipient address has no way to know that your address as sender on the message is fake (i.e. that the message didn't actually come from you). It can send a bounce/non-delivery notification only to the sender it sees on the message ... so you get them. The message of question may be non-deliverable because the recipient is no longer a valid address, or it may be an infected message and blocked by the receiving server's antivirus scanning. Some server-side antivirus, in an attempt to be helpful by notifying of infections, is configured to send a notice to both the sender and recipient.

dadoes, I think your imagination has led you to wild guesses only.

This situation can happen when a spammer finds and and then spoofs a real email address. That's why there's a mountain of no-delivery notices.

I agree with zep, changing your password is a first start. If that doesn't stop the flood, you'll need to abandon this email address and create a new one.

Thank you all. I will change my password immediately.

"Hundreds of emails from "postmaster@mail.hotmail.com" saying email can't be delivered, to people I never heard of and haven't sent any emails to."

You have been "joed" ... some spammer, somewhere, used YOUR e-mail address as the FROM on the spam. So when it bounces, it bounces to you.

One other thing it could be, based on an experience I had a couple years ago - did you happen to sign up for any notifications or email lists in the few days before this happened? I signed up for an email list on a rock singer's website. I don't know if I checked a wrong box or what, but the next day I had literally thousands of emails in my inbox that had been sent to the singer's website. I figured it out, removed myself from the email list and the problem stopped.

Spam. Report to your email provider or ISP (if they provide your webmail).