Is Slavery intrinsically evil? Is it the type of act that is immoral in and of itself, by the very nature of the act? The answer depends on how you define slavery.
If you use the term slavery broadly, to include indentured servitude and requiring criminals to work, then you could not say that slavery was intrinsically evil (in itself immoral). For you would have defined the term so as to be, in some cases, not inherently immoral. Indentured servitude was a necessary, though imperfect, social form, especially in ancient times. When people claim that the Bible approves of slavery, what they are usually referencing is the acceptance, in the Bible, of some forms of indentured servitude.
However, if you define slavery narrowly, so as to include only those types of acts that deprive the human person of his or her fundamental human rights, then slavery is intrinsically evil; it is the type of act that is immoral, in and of itself. In this definition, the moral object of slavery would be the deprivation of fundamental human rights from the human person. The direct and deliberate choice of such an act is intrinsically evil and always gravely immoral.
The Magisterium has not condemned indentured servitude, because indentured servitude is not inherently immoral. It is a very imperfect, but sometimes necessary social form. But the Magisterium has long condemned the severe form of slavery, which is slavery narrowly defined, and which excludes moderate forms such as indentured servitude or requiring convicted criminals to work.
Pope Leo XIII: “This zeal of the Church for liberating the slaves has not languished with the passage of time; on the contrary, the more it bore fruit, the more eagerly it glowed. There are incontestable historical documents which attest to that fact, documents which commended to posterity the names of many of Our predecessors. Among them Saint Gregory the Great, Hadrian I, Alexander III, Innocent III, Gregory IX, Pius II, Leo X, Paul III, Urban VIII, Benedict XIV, Pius VII, and Gregory XVI stand out. They applied every effort to eliminate the institution of slavery wherever it existed. They also took care lest the seeds of slavery return to those places from which this evil institution had been cut away.” (Pope Leo XIII, Catholicae Ecclesiae, Encyclical on Slavery in the Missions, n. 1.)
However, this type of unequivocal condemnation of slavery was only applied to the narrow form of slavery. Pope Pius X refers to slavery in the narrow sense as “slavery, properly so called.” He thereby excludes such forms as indentured servitude, and various other types of limited subjection and servitude.
Pope Pius X: “It is true that soon afterwards the worst of these indignities that is to say, slavery, properly so called — was, by the goodness of the merciful God, abolished; and to this public abolition of slavery in Brazil and in other regions the excellent men who governed those Republics were greatly moved and encouraged by the maternal care and insistence of the Church.” (Pope Pius X, Lacrimabili Statu, Encyclical on the Indians of South America to the Archbishops and Bishops of Latin America, n. 1.)
More on this topic in my book:
The Catechism of Catholic Ethics: A work of Roman Catholic moral theology