Postfix mail for domain.com loops back to myself Error and Solution

I can send and receive mail using user@example.com, but system generated emails such as root@mail.example.com bounce backup with an error:

May 1 03:14:52 mail postfix/smtp[62798]: 23CA4BD6B40: to=, relay=none, delay=0.01, delays=0/0/0/0, dsn=5.4.6, status=bounced (mail for mail.example.com loops back to myself)

How do I fix this error?

Postfix did found a dns reply to your email server, but it hasn't been configured to deal with address such as root@mail.example.com. In other words, your server is configured to accept user@example.com but not as user@mail.example.com. This is well known config problem with virtual domain. To fix this error either add system FQDN to mydestination or relay_domains. Postfix accepts mail for domain listed in virtual_mailbox_domains, virtual_alias_domains, and domains that resolve to IP addresses listed in inet_interfaces and proxy_interfaces. Update mydestination using postconf or by editing main.cf file:

mydestination = localhost.$mydomain, localhost, mail.example.com

Once done reload postfix:
# service postfix reload