Can You Put Hyperlinks In Text Messages?

The SMS/MMS technology itself is not capable of putting HTML hyperlinks in a text message. You can however put regular links in a text message (SMS).

If you have a lengthy link, you can also use ProTexting's Short URL to save on characters.

It is not possible to embed a hyperlink in MMS image.  You can add a regular link or short URL in the MMS message body.