Origen writes in the prologue to his Commentary on the Song of Songs:
For this reason, therefore, I advise and counsel everyone who is not yet rid of the vexations of flesh and blood and has not ceased to feel the passion of his bodily nature, to refrain completely from reading this little book and the things that will be said about it. For they say that with the Hebrews also care is taken to allow no one even to hold this book in his hands, who has not reached a full and ripe age. And there is another practice too that we have received from them--namely, that all the Scriptures should be delivered to boys by teachers and wise men, while at the same time the four that they call deuterōseis--that is to say, the beginning of Genesis, in which the creation of the world is described; the first chapters of Ezekiel, which tell about the cherubim; the end of that same, which contains the building of the Temple; and this book of the Song of Songs--should be reserved for study till the last. (trans. Lawson, p. 23)[In a note (pp. 313–14 n. 7), Lawson explains the term deuterōseis--which often, in the singular, is the patristic way of referencing the Mishnah, but here the term is plural--as apparently implying that the four books or sections of scripture mentioned here should be reserved for a "second" stage of study.]
Jerome, in the prologue to his Commentary on Ezekiel (314 CE), gives the same list of books, and specifies the age at which Jewish boys can read these scriptures.
For unless someone among them has fulfilled the age of priestly ministry, i.e. thirty years old, he is permitted to read neither the first parts of Genesis nor the Song of Songs nor the opening or closing of this book, so that a time of maturity [lit: a time full of human nature] is added to perfect knowledge and mystical understanding.Earlier in his Ep. 53 to Paulinus of Nola, Jerome had said something similar, without mentioning Song of Songs:
The beginning and ending of Ezekiel [...] are involved in so great obscurity that like the commencement of Genesis they are not studied by the Hebrews until they are thirty years old. (Ep. 53.8.16)This is all the evidence for this practice that I know about. I'm not aware of any Jewish evidence.
The statements from Jerome and Origen certainly cannot apply to Jews today (just ask them), or for more than a millennium. Jews read Song of Songs publicly during Passover, a practice attested first in the post-talmudic tractate Soferim 14.
Is there any truth to the tradition as reported by Origen and Jerome? Well, those particular parts of scripture are considered "difficult" or "dangerous" in some rabbinic accounts. (I don't want to look up the references right now. Look in a commentary.) But I do notice that Origen reports this tradition as something "they say," as if he hasn't gotten this information straight from a Jewish source. Very possibly Jerome has read this passage in Origen and simply repeats it without doing his own research. On the other hand, it's not impossible that some group of Jews in antiquity restricted the reading of these scriptures until age 30. That's not a very strong statement, I know.