The evidence would suggest that it was painted in Venice around 1459-65. The dating of the painting is based on two facts - the style (his early style, see below) and the fact that it is a tempera painting (egg paint on board...i.e. before Giovanni Bellini started using oils). Giovanni Bellini was mostly working in Venice and the painting was believed to have belonged to the British Consul Joseph Smith in Venice before it was brought to the UK.
It is, however, painted in the Paduan style. In his early years, Giovanni Bellini spent some time in Padua with his father Jacopo and his brother-in-law, the Andrea Mantegna. This painting is very much in the style of Mantegna, and echoes Mantegna's own painting of the Agony in the Garden. G. Bellini is believed to have left Padua (to return to Venice) around 1460, so, given the estimated dates of the painting (and the fact that Bellini was a very slow painter) , the chances are that it was more likely to have been completed in Venice (although early work/sketches could easily have been Paduan, it should be noted that both Mantegna's and Giovanni Bellini's Agony were actually based on a sketch by Jacopo Bellini)