375 B.C.   Greece
The first significant written account of a proposal to censor music is found in Plato's 'Republic', written in roughly 375 B.C. In one of the most famous passages of ancient literature to deal with music, we find Socrates, Plato's mentor and mouthpiece, engaged in a dialogue with Adeimantus (an elder brother of Plato), describing which of the eight musical modes he would eliminate from the training regime of the rulers ("guardians") of his ideal state. Socrates then goes on describe the musical instruments and rhythms he would include and exclude from his ideal city.
Source: Marie Korpe, Ole Reitov, and Martin Cloonan: 'Music Censorship from Plato to the Present' in: 'Music and Manipulation' (ed. Steven Brown and Ulrik Volgsten), 2006, Berghahn Books.

300s. Europe
At the dawn of Christianity, instrumental music was associated with sensual heathen cults, the theatre and the circus. The human voice was deemed to be more in accordance with piety. After the late 4th century there was an ecclesiastical ban on female singing in the liturgy.

1098–1179. Germany
During a period when female singing was banned in the Christian church, the nun Hildegard von Bingen created 80 compositions to be performed by the nuns of her convent, a type of early oratorio for women's voices. Music was extremely important to Hildegard, and the ban was particularly painful to her. She wrote strong words to the canons and still-absent bishop, reminding them that those who silence God's praises in this life will most assuredly be relegated in the afterlife to "the place of no music." The problem dragged on for many months, until the interdict was finally lifted in March of 1179.