Hamilton, whose grandfather is from the Caribbean island of Grenada, was taunted with cries and banners ranging from 'Stop talking shit', to 'hijo de puta' (son of a whore) and 'negro de mierda' (black shit).
"The FIA is surprised and disappointed at the abuse directed at Lewis Hamilton," the FIA spokesman said.
"An act of this kind is a clear breach of the principles enshrined in the FIA statutes and any repetition will result in sanctions," he added.
The Spanish sports daily Marca also reveals that Alonso, despite clashing with his former teammate Hamilton at McLaren last year, does not condone the behaviour of his countrymen. A source close to the 26-year-old double world champion told the newspaper: "Some of these people are animals."
Updated: Spain condemns Hamilton racism incident
Spain's motor racing federation (RFEA), and the Circuit de Catalunya near Barcelona, have condemned the racist abuse of Lewis Hamilton by spectators at the formula one test at the weekend.
The statements come after the sport's governing FIA warned of possible sanctions, including threats to the status of Spain's two grands prix, at Barcelona and the port city, Valencia.
"The Federation wants to show its absolute repulse at these incomprehensible events," an excerpt from the RFEA's statement on Monday read.
"These kind of madmen who confuse sporting rivalry with violence must know that the Federation will have no tolerance with them," it added.
The Circuit de Catalunya in Montmelo, meanwhile, said it also backs the FIA's position against discrimination of all sorts, and vowed to lodge an official report with the governing body as requested.
"The Circuit de Catalunya will not allow even the smallest incident to repeat itself within its facilities, and new measures are currently being taken into consideration in addition to those implemented during the latest sessions," the Spanish grand prix host said, also refusing to rule out taking legal action against those who perpetrated the abuse.