The discovery was made near the Cardiff Castle end of Queen Street shortly before 6am.
Police said the man arrested was 20 and from the Gwent area.
He was reportedly detained at 6:15am - not long after police had arrived at the scene.
"A man has been arrested and is currently in police custody and police are not looking for anyone else in connection with this incident at this time.
"Further information will be released when available and appropriate."
A Welsh Ambulance Service spokesperson said: "We had a call at approximately 5.50am this morning, Wednesday 28 September 2016, to an incident in the Queen Street area of Cardiff.
"We sent a paramedic in a rapid response car, three emergency ambulances and the Trust's Hazardous Area Response Team to the scene."