Police said no motive has been established for the murder of Venezuelan Cedeno Roroba outside the UN High Commission for Refugees (UNHCR) building in Woodbrook on Thursday.
Speaking with Newsday, investigators said little was known of Roroba, as they are trying to determine if he has relatives in Trinidad.
A man in his early twenties was arrested minutes later at the Mucurapo Cemetery.
In a statement sent to the media, the UNHCR expressed condolences to the family.
"UNHCR is deeply saddened by the shooting death of an asylum seeker from Venezuela in Port of Spain Thursday morning. We offer our sincere condolences to the victim’s family and friends.
"We have confidence that the authorities of TT will conduct an exhaustive investigation into this terrible crime and bring those responsible to justice," UNHCR said.
An autopsy is expected to be done on his body, once relatives are found and are able to identify him.