The Mishnah (Chullin 100bChullin 100b) records a debate between R' Yehudah and the Sages about this. According to the majority view, the verse that records the prohibition was indeed inserted there at the time of the Giving of the Torah - i.e., this is Moshe (speaking in Hashem's name, of course) telling the people: "Therefore, [from now on,] the Children of Israel are not to eat the gid hanasheh..."
Elsewhere (Sanhedrin 59aSanhedrin 59a-bb) the Gemara points out that according to R' Yehudah, gid hanasheh is the only example of a mitzvah that was "given to the Noachides and not repeated at Sinai," and which is therefore binding only on Jews. According to this view, the point is that the Torah didn't need to tell us that Moshe repeated it to the people, because it is obvious that "there is nothing which is prohibited to non-Jews and permissible to Jews" (see also Tosafos there ד"ה ליכא מידעם).