Limassol police were investigating two separate stabbing incidents on Tuesday with one person being treated in hospital in serious condition.
Police said the first incident took place in a house in the Saripolou area at around 7am during an argument.
Officers who went to the scene found a 35-year-old man injured in the abdomen and the back. A 22-year-old also at the scene, was arrested on suspicion of stabbing the man who was rushed to hospital.
The man underwent surgery, and his condition is serious. Officers also collected a large knife from the kitchen.
Reports said both men were from Bangladesh.
Later Tuesday, a 27-year-old delivery man walked into the police HQ with knife injuries to his back and arms.
Before being taken away in an ambulance, the Indian national told officers he had been attacked by a compatriot who had intercepted his moped.
Police were trying to locate the suspect, as it transpired that the two had personal differences.