It is stated in the published Silmarillion and in Letters.
From the Silmarillion: Chapter 24: Of the Voyage of Eärendil and the War of Wrath
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It is told among the Elves that after Eärendil had departed, seeking Elwing his wife, Mandos spoke concerning his fate; and he said: 'Shall mortal man step living upon the undying lands, and yet live?' But Ulmo said: 'For this he was born into the world. And say unto me; whether is he Eärendil Tuor's son of the line of Hador, or the son of Idril, Turgon's daughter, of the Elven-house of Finwë?' And Mandos answered: 'Equally the Noldor, who went wilfully into exile, may not return hither.'
But when all was spoken, Manwë gave judgement, and he said: 'In this matter the power of doom is given to me. The peril that he ventured for love of the Two Kindreds shall not fall upon Eärendil, nor shall it fall upon Elwing his wife who entered into peril for love of him; but they shall not walk again ever among Elves or Men in the Outer Lands. And this is my decree concerning them: to Eärendil and to Elwing, and to their sons, shall be given leave each to choose freely to which kindred their fates shall be joined, and under which kindred they shall be judged.'
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This shows that Mortal Man was not allowed to go to the Undying Lands. When Elros and Elrond made their choices Elros became numbered among Men and therefore was no longer permitted entry to Aman or even The Lonely Isle. Arwen made the same decision to be numbered among Men and therefore could not go to Aman, she would have been refused entry and this she knew.
From Tolkien's Letters:
297 Drafts for a letter to 'Mr Rang'
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(The attempt of Eärendil to cross Ëar was against the Ban of the Valar prohibiting all Men to attempt to set foot on Aman, and against the later special ban prohibiting the Exiled Elves, followers of the rebellious Fëanor, from return:
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325 From a letter to Roger Lancelyn Green 17 July 1971
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The Elves who took this road and those few 'mortals' who by special grace went with them, had abandoned the 'History of the world' and could play no further part in it.
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So unless they were given special permission, Mortals were not permitted to set foot on the Undying Lands.