Maimonides writes in the Laws of Mourning, chapter 4, halakha 4 (approximately as follows): “For the righteous, monuments are not made for them [a structure over the grave—a marker]; their words are their memorial. And a person should not turn himself toward visiting cemeteries.” Although according to the Radbaz there, the explanation in Maimonides is that he rejects only opening the grave, etc., from the Rivash in responsum 421 and elsewhere it seems that according to Maimonides one should indeed not visit cemeteries at all.
In any case, even according to those who permit going, there is the Mishnah Berurah in section 559, subsection 41, which says not to come within four cubits of the grave out of concern that they may cling to it, etc. And see also Bava Kamma 16b regarding Hezekiah, for whom they held a study session at his grave; Tosafot there wrote (s.v. “they held”) that this means at a distance of four cubits, for then there is no “mocking the poor.”

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I am not aware of any prohibition against visiting a grave. Maimonides cannot invent prohibitions on his own.

“Mocking the poor.”

An explicit verse.

“Whoever touches the dead body of any person who has died, and does not purify himself, has defiled the tabernacle of the Lord; and that soul shall be cut off from Israel. Because the water of sprinkling was not dashed upon him, he shall be unclean; his uncleanness is still upon him. This is the law: when a person dies in a tent, everyone who comes into the tent, and everything that is in the tent, shall be unclean seven days. And every open vessel that has no covering fastened upon it is unclean. And whoever in the open field touches one who was slain with a sword, or a corpse, or a human bone, or a grave, shall be unclean seven days.”