Catholic teaching says that there is (at least barring special divine dispensation) exactly one permissible way for human beings to directly produce new human beings: marital mating. This isn't just an arbitrary prohibition--arbitrary prohibitions like the one against pork went out (or, more precisely, underwent aufhebung) when the New Covenant came in. What is the reason for this restriction? We can, after all, permissibly produce other kinds of animals in other ways. There is no Catholic teaching against using artificial insemination in cattle.
I see two options. The first is that it is just the reflexiveness in human beings producing human beings requires the restriction. This seems implausible to me. Imagine that we meet Martians. It would be very odd to think that the Vulcans could permissibly produce new human beings in vitro and humans could permissibly produce new Vulcans in vitro, although humans couldn't permissibly produce humans in vitro (or Vulcans Vulcans).
The second option is that this has something to do with what is special about the target of production: a new human being. But what is it that is special about this target? It seems plausible that it is personhood. This suggests that we are only permitted to directly produce persons by marital mating. (Why? Maybe it has something to do with the more intimate way in which persons are images of God, and hence sacred, as in Paulo Juarez's comment. Or maybe there is a Kantian argument that other forms of production would fail to treat the persons as ends.)
But now if we were to generate genuine artificial intelligence--not merely computers acting as if they were intelligent--then we would have produced a person, and done so apart from marital mating. If I am right that it is personhood that is at the root of the prohibition on in vitro fertilization, it seems to follow that (at least barring special divine dispensation) it is impermissible for us to produce genuine artificial intelligence (AI).
Should this ethical constraint hamper AI research? That depends on whether there is significant reason to think that computers could ever actually have genuine intelligence. If dualism is true (and Catholicism entails dualism), then the only way a computer could gain genuine intelligence, as opposed to merely behaving like an intelligent thing, would be by gaining a soul. But perhaps God has enacted something like a law of nature by which whenever matter is organized in such a way that it could support intelligence, then that matter comes to be ensouled. If so, there could be an ethical problem in aiming at genuine artificial intelligence, and this could ethically restrict AI research since we might not know where the line of sufficient organization would be crossed (presumably, though, we're not that close to the line yet).
Maybe, though, things aren't so simple. Maybe rather than there being a general prohibition on our producing persons except by marital mating, what we have is a general prohibition on our directly producing persons by means other than the natural direct means for originating those kinds of persons. For humans, the natural direct means for origination is marital mating. But for intelligent computers, factory production could perhaps be the natural means for originating. Maybe, but I find more plausible the idea that we simply do not have the right to make persons, except by marital mating.