The Gemara in Masechet Shabbat (28) establishes that when it comes to “Melechet Shamayim” – articles designated for the service of G-d – non-kosher species of animal may not be used. Thus, for example, as the Gemara notes, the parchment for the Tefillin must come from the hide of a kosher species of animal, and parchment produced from a non-kosher species is disqualified. Moreover, the boxes of the Tefillin, the Tefillin straps, as well as the stitching used to sew the Tefillin, must also be produced specifically from a kosher species of animal.
On the basis of this Halacha, the Ran (Rabbenu Nissim of Gerona, 1320-1376), in Masechet Rosh Hashanah, rules that the horn of a non-kosher species of animal may not be used for the Misva of Shofar on Rosh Hashanah. Just as all parts of the Tefillin must be produced from a kosher species, the Shofar must likewise be the horn of a kosher animal.
The Aruch Ha’shulhan (Rav Yehiel Michel Epstein of Nevarduk, 1829-1908) raises the question of how to reconcile this Halacha with the Gemara’s ruling in Masechet Succa that one can, technically, use an elephant as a wall of the Succa. This ruling clearly shows that a non-kosher species of animal may be used to make articles used for Misvot. Seemingly, a Succa wall, which does not have intrinsic Halachic sanctity but facilitates a Misva, should be no different from a Shofar, which is not considered “sacred” but is an article used for a Misva. If non-kosher animals may be used for the Succa walls, why can’t a non-kosher animal be used for the Shofar?
The Aruch Ha’shulhan answers by distinguishing between Misvot that require using material from an animal, and other Misvot. The Succa walls may be used from any materials, and not necessarily from material taken from animals, and therefore there are no restrictions on which kind of animal may be used. The Shofar, however, must be the horn of an animal, and Tefillin similarly must be produced from animals. When it comes to these Misvot, then, non-kosher animals may not be used.
As for the practical Halacha, the Rama (Rabbi Moshe Isserles of Cracow, 1525-1572) rules (Orah Haim 586) that the horn of a non-kosher animal may not be used for the Shofar. However, the Mishna Berura (Rav Yisrael Meir Kagan of Radin, 1839-1933) adds that the Rama’s ruling is not universally accepted, as some Halachic authorities distinguish between the Tefillin, on which the words of Torah are written, and other Misva articles. Therefore, if one does not have a Shofar from a kosher species, he may use a Shofar taken from a non-kosher species, but without reciting the Beracha.