Police said the incident happened in Green Lane at around 8pm.
A man was then arrested and a knife recovered from the scene, police added.
A Sussex Police spokesperson said: “Police were called to a report of a stabbing in Green Lane, Chichester, about 8pm on Friday, March 31.
“Officers responded to the scene and following a search of the area, a suspect was detained in The Hornet and a knife was recovered.
“The 32-year-old man, from Chichester, was arrested on suspicion of committing grievous bodily harm and possession of a knife in public. He remains in police custody.
“A 28-year-old local man self-presented to hospital, where he was treated for an arm wound.
“Enquiries into this isolated incident are ongoing and the public can expect to see an increased police presence in the area in the meantime.
“Anyone who witnessed what happened is asked to report it online or call 101, quoting serial 1264 of 31/03.”
1. Armed police at the scene in Chichester on March 31, 2023
Armed police at the scene in Chichester on March 31, 2023. Picture by Eddie Mitchell Photo: Eddie Mitchell
2. Armed police at the scene in Chichester on March 31, 2023
Armed police at the scene in Chichester on March 31, 2023. Picture by Eddie Mitchell Photo: Eddie Mitchell
3. Armed police at the scene in Chichester on March 31, 2023
Armed police at the scene in Chichester on March 31, 2023. Picture by Eddie Mitchell Photo: Eddie Mitchell
4. Armed police at the scene in Chichester on March 31, 2023
Armed police at the scene in Chichester on March 31, 2023. Picture by Eddie Mitchell Photo: Eddie Mitchell