Usually you have to find an ISP which allows you to send him a message, and then the ISP can translate it to SMS and forward it to the subscriber.
AFAIK usually this is done by sending an e-mail to a certain address with some special subject of message body formatting. This is mostly a paid service though.
The problem is not in Linux, but in find someone who provides you the service. Once such a provider is found, it should be easy. For example, Cisco switches send SMS-es all the time.