וַיָּ֨מָת שָׁ֜ם מֹשֶׁ֧ה עֶֽבֶד־יְהוָ֛ה בְּאֶ֥רֶץ מוֹאָ֖ב עַל־פִּ֥י יְהוָֽה׃ וַיִּקְבֹּ֨ר אֹת֤וֹ בַגַּיְ֙ בְּאֶ֣רֶץ מוֹאָ֔ב מ֖וּל בֵּ֣ית פְּע֑וֹר וְלֹֽא־יָדַ֥ע אִישׁ֙ אֶת־קְבֻ֣רָת֔וֹ עַ֖ד הַיּ֥וֹם הַזֶּֽה׃
So Moses the servant of the LORD died there in the land of Moab, according to the word of the LORD. And he was buried in the valley in the land of Moab over against Beth-peor; and no man knows of his grave unto this day (translation from Sefaria, mostly).
As for why Hashem acted in this manner:
1) The Bayit Chadash (Bach) on Sotah 14a states that Hashem knew in advance that He would destroy the Temple and exile Bnei Yisrael, and if He had informed them of Moshe's grave site, they would have prayed there, and Moshe would have entreated Hashem (successfully) to repeal the decree. Assumingly, if Bnei Yisrael cannot pray at his grave, then he, the greatest defense attorney of the Jewish people (see Cheit Ha'Egel, Meraglim, Korach) cannot come to their aid.
2) Rav Shimshon Refael Hirsch explains that it was so that his grave site would not become a shrine and he would not be worshiped, in the manner that other religions tend to act (Christianity, for example).
(Thank you to @Baby Seal for pointing me to the Bach.)