The man was wanted in connection with an incident of racial abuse that took place at 10.45am on September 22.
A 32-year-old woman had reported a man shouting racial abuse at her as she walked past him in Palmerston Avenue, Fareham.
Fareham police posted on social media they had arrested the 33-year-old man, of no fixed address, after finding him in West Street.
Officers said they said he was also arrested on suspicion of having heroin, a class A drug, when he was discovered on Tuesday.
A spokeswoman from Hampshire Constabulary said: ‘Officers were on patrol on West Street, Fareham, when they saw a man they suspected to be involved.
‘The suspect, a 33-year-old man of no fixed abode, was arrested on suspicion of racially aggravated harassment and possession of a Class A drug after suspected heroin was found on his person.
‘He has been released from custody on police bail as the investigation continues.’
It comes after Fareham Borough Council introduced measures to tackle anti-social behaviour in the town centre this year, including private security guards to patrol the area.