You can edit /etc/drweb/drweb_qmail.conf to eliminate receiving notification messages when Dr. Web has an issue:
[VirusNotifications]
SenderNotify = no
AdminNotify = no
RcptsNotify = no
Then just restart Dr. Web with:
/etc/init.d/drwebd restart
Plesk has a KB article about this issue as well.

Thanks for the post, this has been driving me nuts..
In my case the file which needed to be edited was /etc/drweb/drweb_handler.conf
My steps:
cd /etc/drweb
nano drweb_handler.conf
Thanks again.
In my case, filename was slightly different.
The filename was;
/etc/drweb/drweb_handler.conf
Thanks, it works.
On CentOS 5.5 x86_64 with PPP 9.5 the filename is: /etc/drweb/drweb_handler.conf
Parallels should fix this and let customers make the desired changes in the gui.....
Thank you very much.. It works.. Nice help... Cheers..