Born in Dos Aguas, Valencia Province, Barberá began his World Championship career at the age of 15 in the 2002 125cc world championship, under the guidance of Jorge Martínez "Aspar", who teamed Barberá and fellow youngster Ángel Rodríguez up with the experienced Pablo Nieto.

In his first season Barberá established himself as the most promising rider of the three and in 2003 he broke through, with his first victory at Donington Park making him one of the youngest riders ever to win a Grand Prix. A strong finish to the season saw him take third place in the championship and he signed up for a title challenge with Seedorf Racing in 2003. Several inopportune crashes and mechanical failures derailed his hopes but victory in the final race secured the runner-up spot and a factory ride with Fortuna Honda in the 250cc class for 2005. After two years with the team he moved to Team Toth in 2007.

Barberá survived a huge crash during the Italian round of the championship on June 1, 2008. Running second behind Marco Simoncelli on the penultimate lap who tried to defend his lead by changing his line on the straight, Barberá slipstreamed onto Simoncelli's back wheel and clipped it with his front brake lever. His bike somersaulted through the air, with Barberá escaping somewhat uninjured. However, a further crash in practice at Motegi left him with two spinal fractures, ending his season.

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