Barberá began his World Championship career at age 15 in the 2002 125cc class under the guidance of Jorge Martínez "Aspar". He established himself as one of the most promising young riders in the paddock, scoring his first Grand Prix victory at Donington Park in 2003 to become one of the youngest winners in the class's history. A strong finish to that season placed him third in the championship.
In 2004 he challenged for the 125cc title but several untimely crashes and mechanical failures cost him dearly, though victory in the final race secured second place in the standings. He then moved up to 250cc with a factory Honda ride for 2005.
After two seasons with Fortuna Honda in the 250cc class, Barberá moved to Team Toth for 2007. His 2008 season was cut short when he suffered two spinal fractures in a practice crash at Motegi, ending his year prematurely. He had already survived a dramatic accident at Mugello earlier that season when a collision with Marco Simoncelli sent his machine somersaulting through the air.
The 2009 season was his finest in 250cc. Barberá won three races and collected five additional podiums to finish second in the championship behind Hiroshi Aoyama. Memorably, he won the 2009 Valencia Grand Prix — the final 250cc Grand Prix in history, as the class was discontinued in favour of the four-stroke Moto2 format from 2010.
Barberá moved to MotoGP in 2010 with the Aspar Team riding customer Ducati machinery. He finished 12th in the championship in his debut premier class season and 11th in 2011, establishing himself as a consistent midfield presence. He moved to Pramac Racing for 2012, where he spent several seasons.
His career best result in the MotoGP standings came in 2016, when he finished tenth overall. That year also saw his only appearances for a factory MotoGP team: he twice substituted for the injured Andrea Iannone at Ducati Corse. After failing to secure a MotoGP ride for 2018, Barberá switched to Moto2. He competed in his final Grand Prix at Mugello in 2018.
Barberá's career was repeatedly disrupted by legal matters off the track. He received a six-month jail sentence for assault and battery in 2013. In 2018, a drink-driving conviction resulted in 22 days of community service and cost him his Pons Racing Moto2 seat. In 2019, he was accused of stealing a Yamaha Supersport bike belonging to his own team, Team Toth. Further investigations into fraud and forgery emerged in 2023, along with reports of an outstanding arrest warrant dating to 2019.
After his Grand Prix career concluded, Barberá competed across a range of series including the Superbike World Championship, World Supersport, British Superbikes, and MotoAmerica, where he currently races aboard a BMW S1000RR.