There was such an ordinance in 1543 banning the export of novels to the New World, but it was not about the settlers, but about the Indians. The whole idea behind it was that the natives were still being "doctrinated", learning the good teachings, etc.

This "doctrination" was done using books (I know it is obvious, but it makes sense in context), more precisely religious books such as Bibles, Gospels, books of saints, and religious literature in general, most notably texts by the Fathers of the Church. In that state of affairs, as the books being used were considered to be the truth and nothing but the truth, the preachers and teachers thought that by introducing works of fiction, the Indians would not be able to tell apart which books contained real stories and which did not, and so they would learn "vices and bad habits". So, as a profilactic measure, the export of works of fiction to the New World was banned.

The ordinance is very interesting, so I am going to translate for the enjoyment of any passersby of this sub:

Charter ordering not to tolerate the bringing of books of profane stories to the Indies

The King. President and magistrates of our Audience and Royal Chancellery of our provinces of Perú, We are informed that in case of being taken thither any books of profane romances, and fables, such as the Amadís and others of the same quality of lying stories, many inconveniences shall follow: because the Indians that would know how to read, giving themselves to them, would abandon those of good and holy doctrine, learn in them the bad habits and vices, and furthermore knowing that those books of vain stories have been composed without those things having thus happened, it could be that they would lose belief in the Holy Scriptures and other books by the Doctors, believing, as people not rooted in the Faith, that all our books were of the same authority and manner. And so that those inconveniences and others that may arise be avoided, I command you to not tolerate that in those lands be such books sold, nor be there any such books whatsoever, neither be them brought there anew; and that you shall provide that no Spaniard should have those books, nor any Indians read them, so that those inconveniences may cease.

Given in the town of Valladolid, the twenty-ninth of September, year 1543. I, the Prince, by His Majesty's command. His Highness in his name. Juan de Sámano. Stamped by the Council.

These were not the only forbidden books in the Americas. There are other Royal Ordinances explicitly stating that no books forbidden by the Inquisition should be exported to the Indies, nor books forbidden by the Council of the Indies.

The laws on books that should go or not go to the Indies are a very intersting read, and one can find it in the Cedulario Indiano, also known as Cedulario de Encinas, thus called in honour of the very diligent Diego de Encinas who compiled the laws and ordinances. For example, in 1548, the export of books to the Indies became tax exempt, as they would be useful in the education of people. Not long after, the universities of Mexico and Lima were created in order to locally source the lawyers necessary for the proper functioning of the administration.