Every portal has a "portal administrator" user.
Here's what you can do: create a new user (Customize>Users) in your account called "noreply", with this email address. This user does not need sign in rights, so they are a free user).
Then go to Customize > Portals and edit your portal. Set the portal administrator to the noreply user.
BUT...I would caution you about this. Do you *really* want to do this? If a user has trouble signing up for your portal, the 'contact us' registration form goes to the same portal administrator. Also emails coming from the portal, such as cases and payment notifications are coming from this user too. Having them come from a noreply email address might mean some frustrated customers who find its hard to get hold of you.
What we do here at Method HQ, with our portal, is have a special customer service email address and user, and that email address automatically distributes to everyone on our team who handles customer service. That way everyone gets a notification and the first person available jumps on it.
HTHs,
Paul