In truly ancient Israel (i.e., before Roman times), emphatically no.
To quote from Nurit Yaari’s forthcoming book, Between ʻJerusalemʼ and ʻAthensʼ: Israeli theatre and the classical tradition* (Oxford University Press, in press):
Theatre, as an art, a community event and a cultural institution, is entirely ‘Athens’ in nature: that is where it was first created in the late sixth century BCE, and where it acquired its form, conventions and concepts. As a visual and performative art, it is rooted in all aspects of classical Greek art—poetry, music, dance, sculpture, painting and architecture; indeed, their fusion is what gave rise to this independent and unique art form. […]
[T]heatre is intrinsically alien to ‘Jerusalem’—both as an art form and as a cultural institution. Herod (the Great) introduced Roman theatre into Judea as a form of public entertainment in the Second Temple period, when he incorporated one in the seaside town of Caesarea that he built between 22 and 10 BCE and dedicated to Augustus, the Roman emperor. Subsequently, he is said to have built another one in Jerusalem (although it has yet to be found). By the third century CE, many such Roman theatres had been built throughout the country —but performances were attended mostly by the non-Jewish population.
Throughout the history of Jewish culture, theatre oscillated furtively between prohibition and fascination. Even a cursory survey of the history of Jewish culture is sufficient to note the conspicuous absence of a theatrical tradition. Indeed, the very term ‘Jewish theatre’ might be regarded an oxymoron, since it ostensibly violates the second commandment’s prohibition of any kind of representation
It is only in the aftermath of the Jewish Enlightenment movement at the end of the eighteenth century and the religious reforms of the early nineteenth century, that Yiddish theatre emerged in the final quarter of the nineteenth century, as a form of popular entertainment for Jewish communities of central Europe. Hebrew theatre, for its part, emerged at the beginning of the twentieth century in Moscow and [Palestine] as a key contribution in the rebirth of Hebrew as a living language and the realisation of Zionist vision and Jewish national aspirations.
So there you have it.
That said, in Israel—today, and in biblical times, if the Old Testament stories are anything to go by—life itself is theatre, so there’s little need to go to a designated ‘theatre’ to watch it.
Israelis (not unlike Brits, come to think of it) love drama, and enact it on a daily basis in public and at home, and at high volume (unlike Brits). Monty Python’sunwittingly captured the spirit of everyday life in Israel (then and now) far more accurately than any romanticised Leon Uris novel, or any modern-day earnest documentary about the Holy Land.
Case in point: a Canadian friend of mine recently saw a party of Israelis having a picnic in the park, and remarked to me, in worried tones:
‘Oh, dear,’ he said to me. ‘Looks like they’re breaking up—they’ll be coming to blows, at this rate.’
‘Not at all,’ I laughed. ‘They’re having a great time together.’
* Full disclosure: I translated it from the Hebrew
(Originally written in reply to a question at Quora.com)