Gabriel Escarrer said the apartment listings website was the biggest risk facing global tourism during a meeting of businesspeople in Barcelona on Thursday.
Escarrer said that Barcelona would be a "victim of its own success" if it failed to address the problem of Airbnb.
"As it is not regulated, it is killing Barcelona's exemplary tourism model," Escarrer said, according to Spanish newspaper, Expansión.
There has been an ongoing row in Spain over whether Airbnb holds the necessary permits to operate in the country.
In December 2015, the company was fined by Barcelona's City Hall for marketing lodgings that lacked permits to hold tourists.
With the aid of a software programme, the town hall detected listings for 1,891 lodgings that did not have proper permits on Airbnb, and another 3,929 on HomeAway, another listings website, it said in a statement.
Each have been issued a fine of €60,000 ($65,000).
Since taking office in June, Barcelona mayor Ada Colau, a former anti-eviction activist, has kept her pledge to try to curb a boom in visitor numbers that she fears could drive out poor residents and spoil the charm of Spain's second largest city.
But despite this, Escarrer claimed there was "little willingness to tackle the problem" posed by Airbnb.
The number of visitors to the city has skyrocketed from 1.7 million in 1990 to 7.4 million last year, making Barcelona the third most-visited city in Europe, after London and Paris.
Melia Vicepresident Escarrer warned that the current tourism model in Barcelona was unsustainable.
Melia International was founded in 1956 in Mallorca and is Spain's biggest hotel operator and the 17th biggest in the world.