The two cars were burned in the city's Sant Martí district on Monday, Catalan daily La Vanguardia reported.
"It's a relief no one was injured but these acts of violence can never be justified in a democracy," sources at Uber said.
Barcelona's Elite Professionals Taxi Association, which staged protests against the app on Monday, condemned the burning of the cars while asking the regional government to take serious action against Uber so that such incidents would not take place again.
But association spokesperson Alberto Álvarez said the group would continue to "make noise", protesting in a legal manner against Uber, as well as against other "pirate drivers" and the passivity of the Catalan government.
Taxi drivers in Madrid and Barcelona have gone on strike on a number of occasions in recent months, protesting against a service they see as unfair competition.
The service is illegal in both cities, with drivers liable for fines of up to €18,000 ($32,000) in Madrid, and €6,000 in Barcelona.
A spokesperson for Uber in Spain recently told The Local. "We believe that there’s room for everyone, and we’re improving transport options for both passengers and drivers alike."