In the framework of the expected association between gamma-ray bursts and gravitational waves, we present results of an analysis aimed to search for a burst of gravitational waves in coincidence with gamma-ray burst 050915a. This was a long duration gamma-ray burst detected by Swift during September 2005, when the Virgo gravitational wave detector was engaged in a commissioning run during which the best sensitivity attained in 2005 was exhibited. This offered the opportunity for Virgo's first search for a gravitational wave signal in coincidence with a gamma-ray burst. The result of our study is a set of strain amplitude upper limits, based on the loudest event approach, for different but quite general types of burst signal waveforms. The best upper limit strain amplitudes we obtain are Hz-1/2 around ∼200-1500 Hz. These upper limits allow us to evaluate the level up to which Virgo, when reaching nominal sensitivity, will be able to constrain the gravitational wave output associated with a long burst. Moreover, the analysis presented here plays the role of a prototype, crucial in defining a methodology for gamma-ray burst triggered searches with Virgo and opening the way for future joint analyses with LIGO.