The body was discovered by divers for the Compañía Auxiliar del Puerto (CAPSA) who were cleaning the sea wall in Santa Cruz de Tenerife.
The suitcase contained a male torso wrapped in plastic bags, missing its head and limbs.
The beach, which was full of sunbathers, was immediately closed while police carried out forensic tests.
The Civil Guard arrested a boy of Brazilian nationality on Monday afternoon for the suspected murder of his father, according to newspaper El Español.
He is suspected of throwing the suitcase into the sea on Monday, May 30th.
Locals told police they had seen a young man "perhaps of Moroccan or South American origin" carrying a suitcase - or two, according to some witnesses - close to the sea that night. He asked locals where the best place was to access the sea.
Eyewitness testimony and forensic evidence (the body in the suitcase was found to be South American) led police to a house in the Salamanca neighbourhood of the city, where the man lived with his son.
Police revealed the son and father most probably had a fight, which resulted in the son killing the father, chopping up his body and throwing it into the sea.
Police sources confirmed that when searching the house of the suspect they discovered evidence of the having been chopped up.