Error messages can be both confusing and misleading.
Since you note that you have quite heavy traffic, perhaps you can increase the open-files-limit to more than 10,000 ??
Indeed! FOr the OP and any future readers:
The process to increase open_files_limit is different depending upon your OS...
http://duntuk.com/how-raise-ulimit-open-files-and-mysql-openfileslimit (centos 6, and likely earlier)
https://ma.ttias.be/increase-open-files-limit-in-mariadb-on-centos-7-with-systemd/
Google is your friend... so is dba.stackexchange.com and http://community.spiceworks.com/databases and the like... hope you got your issue resolved =)