In Ruach Chaim by Rabbi Chaim Palagi (Siman 566), he is stringent on this matter and brings proof for a prohibition. However, in practice, the authorities rule leniently, and therefore one may get a haircut both on the eve of the fast and on the fast day itself, as written by the Turei Even (Rosh Hashanah 18a) that there is no mention in the Halachic authorities to forbid this. Nevertheless, a pious soul (Ba’al Nefesh) should be stringent not to get a haircut on the 17th of Tammuz itself, as Maran the Mishnah Berurah (Siman 550) wrote that we apply stringencies to the 17th of Tammuz similar to Tisha B’Av.