Objection 1. It would seem that Penance is not a sacrament. For Gregory [Cf. Isidore, Etym. vi, ch. 19] says: "The sacraments are Baptism, Chrism, and the Body and Blood of Christ; which are called sacraments because under the veil of corporeal things the Divine power works out salvation in a hidden manner." But this does not happen in Penance, because therein corporeal things are not employed that, under them, the power of God may work our salvation. Therefore Penance is not a sacrament.
Objection 2. Further, the sacraments of the Church are shown forth by the ministers of Christ, according to 1 Corinthians 4:1: "Let a man so account of us as of the ministers of Christ, and the dispensers of the mysteries of God." But Penance is not conferred by the ministers of Christ, but is inspired inwardly into man by God, according to Jeremiah 31:19: "After Thou didst convert me, I did penance." Therefore it seems that Penance is not a sacrament.
Objection 3. Further, in the sacraments of which we have already spoken above, there is something that is sacrament only, something that is both reality and sacrament, and something that is reality only, as is clear from what has been stated (66, 1). But this does not apply to Penance. Therefore Penance is not a sacrament.
On the contrary, As Baptism is conferred that we may be cleansed from sin, so also is Penance: wherefore Peter said to Simon Magus (Acts 8:22): "Do penance... from this thy wickedness." But Baptism is a sacrament as stated above (Question 66, Article 1). Therefore for the same reason Penance is also a sacrament.
I answer that, As Gregory says [Isidore, Etym. vi, ch. 19, "a sacrament consists in a solemn act, whereby something is so done that we understand it to signify the holiness which it confers." Now it is evident that in Penance something is done so that something holy is signified both on the part of the penitent sinner, and on the part of the priest absolving, because the penitent sinner, by deed and word, shows his heart to have renounced sin, and in like manner the priest, by his deed and word with regard to the penitent, signifies the work of God Who forgives his sins. Therefore it is evident that Penance, as practiced in the Church, is a sacrament.
Reply to Objection 1. By corporeal things taken in a wide sense we may understand also external sensible actions, which are to this sacrament what water is to Baptism, or chrism to Confirmation. But it is to be observed that in those sacraments, whereby an exceptional grace surpassing altogether the proportion of a human act, is conferred, some corporeal matter is employed externally, e.g. in Baptism, which confers full remission of all sins, both as to guilt and as to punishment, and in Confirmation, wherein the fulness of the Holy Ghost is bestowed, and in Extreme Unction, which confers perfect spiritual health derived from the virtue of Christ as from an extrinsic principle. Wherefore, such human acts as are in these sacraments, are not the essential matter of the sacrament, but are dispositions thereto. On the other hand, in those sacraments whose effect corresponds to that of some human act, the sensible human act itself takes the place of matter, as in the case of Penance and Matrimony, even as in bodily medicines, some are applied externally, such as plasters and drugs, while others are acts of the person who seeks to be cured, such as certain exercises.
Reply to Objection 2. In those sacraments which have a corporeal matter, this matter needs to be applied by a minister of the Church, who stands in the place of Christ, which denotes that the excellence of the power which operates in the sacraments is from Christ. But in the sacrament of Penance, as stated above (ad 1), human actions take the place of matter, and these actions proceed from internal inspiration, wherefore the matter is not applied by the minister, but by God working inwardly; while the minister furnishes the complement of the sacrament, when he absolves the penitent.
Reply to Objection 3. In Penance also, there is something which is sacrament only, viz. the acts performed outwardly both by the repentant sinner, and by the priest in giving absolution; that which is reality and sacrament is the sinner's inward repentance; while that which is reality, and not sacrament, is the forgiveness of sin. The first of these taken altogether is the cause of the second; and the first and second together are the cause of the third.
Source: Summa Theologica (New Advent)