Yes, they did. In fact, they tried to ban any form of public entertainment, including recorded music, dance, cinema etc. The reasons were that they were unislamic and western, hence unsuitable for the Iranian people. You don't sing about sex, drugs and rock 'n' roll, the only thing you're supposed to sing is the Qur'an. In the post-revolution years, the cities were controlled by revolutionary guards, who roamed free and arrested anyone for unislamic behaviour, raided houses etc. So these laws were enforced by terror squads. They still exist, but they are significantly more easy-going than they were thirty years ago.
However, Iranians love to party and they started to do so even harder when they were told not to. The government eventually saw the propaganda value of these media during the war with Iraq, and so they gradually allowed music and movies, under the condition that they are home-made and, of course, government approved. There are also reports of semi-legal underground metal gigs, even though metal is strictly against the law. But pop music et al is fine, as long as it's Iranian. Every once in a while, a western CD hits the Iranian market, though. I recall there was a censored release of Queen's Greatest Hits a few years back, minus all the love songs (no clue how that's supposed to work).