The victim was pronounced dead by paramedics at a recreation ground in the town of Fareham on Wednesday morning.
Emergency services had been called to the scene on Hillson Drive at about 10.25am.
Hampshire Police said officers were speaking to people in the area and carrying out other lines of inquiry to establish how the man died.
A 20-year-old man, who lives locally, has been arrested on suspicion of being the owner or person in charge of a dog dangerously out of control causing injury resulting in death.
He has been released from custody without charge but remains under investigation, Hampshire Police said.
A dog has been secured and removed from the scene, while the victim’s family has been informed.