Two men aged in their thirties sustained injuries as a result of the assault, which happened at Lammas Street. One man was punched, leaving him with a cut in the mouth. The second man was struck with glass, causing a cut to his head.
The incident is thought to have taken place sometime between 4.30am and 6am.
As part of the ongoing investigation, officers are now appealing for anyone who was in the area and witnessed the incident to get in touch.
Anyone with information is asked to contact Carmarthen Police by calling 101. If you are Deaf, hard of hearing or speech impaired text the non-emergency number on 07811 311 908.