The group, based on the Spanish resort island of Tenerife, charged €1,000-€1,500 ($1,350-2,000) for fake Spanish residence permits which allow the holder to enter Mexico without a visa, police said in a statement.
"Once in Mexico the clients used the group's contacts in the north of the country to try to illegally cross the border with the United States, and once there seek residency under the Cuban Adjustment Act," it said.
Under the so-called "wet foot/dry foot" policy of the Cuban Adjustment Act, Cuban migrants who make it onto United States soil are allowed to remain while those intercepted at sea are returned to their home or a third country.
The group solicited clients for its services from a travel agency which it ran in Tenerife, the largest and most populous island of the Canary Islands located off the west coast of Morocco.
Police detained 11 Cubans and three Spaniards as part of the investigation and seized 12 fake Spanish residency permits as well as €13,000 and 3,250 dollars in cash.