It would not have been difficult for ancient machine inventors to apply an automatic playing apparatus to the hydraulis, but there is no source evidence for it. In 9th century Arabia, the three brothers Banū Mūsā invented an automatic pipe instrument controlled by a cylinder, but it was a flute-playing machine rather than an automatic organ, because it had only one pipe with holes that were closed and opened by the machine.
The first known automatic instruments in Western Europe were the automatic carillons of the 14th century. It is not known when the first automatic organs appeared, but by the mid-15th century there were already instrument makers in the Netherlands specializing in automatic organs.[1] In the 17th century, automatic organ building achieved a very high level, and the instruments were described in various books. Salomon de Caus, for example, described the parts and functions of automatic organs in Les raisons des forces mouvantes (1615), and Athanasius Kircher gives many examples of automatic organs with complicated mechanisms in his Musurgia Universalis (1650).

[1] Musical Automata. Catalogue of automatic musical instruments in the National Museum ‘From Musical Clock to Street Organ’, Utrecht 1994, p. 19