There's several Kantian texts to consider on this front and a key question about the nature of "interest."
First, I want to look at "interest." Interest could mean something like
research interest or it could mean something like
fascination or just a mere
hobby. I'm going to assume you don't mean
delight but I want to mention it at various points during my answer, so I'll throw it in there too.
Turning to Kant's texts, as many of the other answers note there's the Groundwork and the many formulations of the categorical imperative that can serve as a test. Two types of formulas seem important here: the universalization tests and the humanity/rationality tests. On most definitions of interest, it doesn't seem immediately contradictory for everyone to take an interest in these things. It seems troubling if we take interest as in
delight but it's not even clear (at least at 10am) that this is by itself contradictory. On a certain level, there may be a practical contradiction (everyone does this plus the laws of nature) which I will mention below.
Looking at the humanity/rationality tests, here we ask whether an action treats another as a means rather than an end, because rational nature ("humanity") always and everywhere deserves to be treated as an end and never merely as a mere means. On this formulation, it's clear some thing likes
delight would be treating other's suffering as a means; other meanings are going to be a little fuzzier, like
research interest seem okay though in that while the suffering of others would be a means to this interest, the interest itself would be oriented towards people as ends.
A second thing to consider in the Groundwork is the difference between perfect and imperfect duties. For Kant, we have a perfect duty to behave in accordance with the categorical imperative, but we also have two imperfect duties -- things where we don't universalize particular acts but do all need to pursue two ends: the perfection of ourselves and aiding others. An interest in tragedies of this sort could reflect an interest in perfecting ourselves and/or aiding others depending on how it works out. If it reflects neither, then it may be immoral for Kant.
Moving away from the Groundwork, there are two other texts that are worth looking at. First, there's the Metaphysics of Morals especially its second half -- "Doctrine of Virtue" (= Tugendlehre) Here, Kant treats on a large number of practical questions and problem cases there.
One case that springs to mind is Kant's response to animal suffering. Kant's view is that we should not enjoy animal suffering because it will numb us and make us indifferent to human suffering. It seems that by extension this would be an important issue to consider in response to interest in terrible events -- namely, that it's wrong if it numbs us to the wrong and horror of these events.
A second text to consider is Kant's Anthropology. Here, the relevant point is that Kant splits anthropology from ethics proper and engages in a study of human behavior as it actually occurs. If your interest falls in a similar vein, it's hard to grasp how Kant could condemn it.