The ring would steal the codes of the credit cards of customers of hostess bars on the beach resort of Magaluf, which is known for its excesses of alcohol and sex, and sometimes clone the cards, Spain's interior ministry said on Tuesday.
The main victims were tourists from Britain and Scandinavia "who were intoxicated, since in this state it is easier to trick them to obtain the security codes of the cards or to carry out a series of charges of a high amount," it said in a statement.
"The amount swindled amounts to over €45,000 (50,000 dollars), although it is suspected that it could be higher since many victims have not filed a complaint," it added.
Police detained four men and 16 women as part of their operation, which involved searches of four hostess bars in Majorca, including two owned by the suspected leader of the ring.
Magaluf, where some 85 percent of holidaymakers are British or Irish nationals, made global headlines last year after a video showing a young woman performing oral sex on several men on the dance floor of a ightclub went viral.
Local authorities subsequently introduced new rules regulating pub crawls and have also banned "balconing" - jumping from one apartment balcony to another or into a swimming pool - after several deaths in recent years.
Last week two British police officers joined their Spanish counterparts in patrolling the streets of Magaluf in a bid to tackle disorderly British holidaymakers.