The victim, said to be be aged between 25 and 30, died after being knifed several times next to an apartment in the centre of the town.
The alarm was raised around 7am on Monday.
Efforts to revive the casualty at the scene proved unsuccessful.
Local reports say a man carrying a knife in his hand with blood on his hands was located and identified inside the nearby flat.
He and his alleged victim are understood to know each other.
His nationality has not yet been revealed.
The Policia Judiciaria is conducting an ongoing investigation.
It is not yet known if the dead man lived in Portugal or was on holiday there, although the flat where the killing occurred has been described as being part of a tourist complex where foreign tourists usually stay.
Monday is a Bank Holiday in Portugal and police there could not be immediately reached for comment.
Officers from Portugal’s GNR force were first on the scene along with paramedics.