Officers said the “altercation” happened around 23:00 on Saturday on the corner of Bond Street and Conway Street, between Kings Bar and the No 10 bar.
They said in a statement: “The incident involved a male and female adult.
“The female was in her 20s, she had dark hair up in a bun, wearing a black vest top on and beige shorts. The male was also in his 20s and was wearing a long-sleeved grey top, light-coloured shorts and white trainers.
“An altercation took place and some minor injuries were caused.”
Anyone with more information is asked to call Police on 612612 or make an anonymous report via Crimestoppers.