In a statement, police said there were "more than a dozen complaints from victims who bought this substance" -- a product that had no "curative effects."
One of them "paid more than €25,600 ($27,200) to treat his daughter," they added.
Among those detained last week are two professors at the University of the Balearic Islands (UIB), a police spokesman in Palma de Majorca told AFP, without giving their identities or detailing what they teach or research.
The three other suspects include two people who worked in the research department of a foundation, he added.
They have been charged with fraud and released pending further investigation.
The suspects are accused of having promoted their anti-cancer drug in ad campaigns on social networks, "taking advantage of the academic and professional recognition brought about by their posts."
But the drug was merely a "placebo" with no sales authorisation, police said.
They added the substance was sold to patients or their families via a non-profit foundation that "covered up the sale of the product as a voluntary donation from relatives for research."
The academics are also suspected of having tried to sell another "fake drug" against Alzheimer's disease, police said.
Jaume Carot, vice chancellor of UIB, said the university had received a written complaint about the issue in April last year, and brought the matter to authorities.
He added the university was "extremely concerned by all this".