There are a number of software solutions that can poll network devices via SNMP and store their MAC address tables in a SQL database. Generally, their functionality includes a great deal more than what you are asking for in your question.

Before installing the software on a server, it is important to note that you should have administrative access to the network devices, or at the very least, permission to query the devices in question. Either you, or your IT support folks, will need to configure the switches with permit SNMP string as well as permit SNMP queries from the server IP/subnet that it resides on. How these device are configured is vendor dependant and beyond the apparent scope of your question.

One example of such a tool available for Ubuntu is Netdisco.

Per their website, Netdisco is a software package that maintains "Configuration information and connection data for network devices [that is] ... retrieved via SNMP. Data is stored using a SQL database for scalability and speed. Layer-2 topology protocols such as CDP and LLDP provide automatic discovery of the network topology."

While there is a package available for install from the Ubuntu repositories (see netdiso-common, netdisco-backend, and netdisco-frontend) it is somewhat outdated. A more recent version can be installed from source on their site.

Another example would be IPPlan which focuses on IP Address Management(IPAM), DNS and circuit management. IPPLAN polls via the ucd-snmp package and NMAP and can map IP addresses to MAC addresses in a variety of SQL databases.

Also, you may want to take a look at Switchmap.

While it does not store its data in SQL, it creates CSV files which can then be poured into a SQL database, if desired.

There are a number of other solutions out there (both commercial and free). I only mention these as I have had direct experience installing, configuring, and managing these software packages.