The definition of “sacrament” that we use customarily is not a biblical definition but is rather a theological or church-determined definition.  Most of the time Lutherans say that there are two sacraments, Baptism and the Lord’s Supper.  And that is right to do.  For the definition of sacrament that Lutherans use is threefold:  a divine rite instituted by Christ in His earthly ministry that gives the forgiveness of sins and uses a visible, physical element.  Under that definition Baptism and the Lord’s Supper most clearly fit.  In the case of the absolution spoken by the pastor, absolution can only be called a sacrament if the visible element isn’t critical.  Of course in Baptism, the Lord’s Supper, and absolution there must be someone there doing the speaking and administration. 

However, our own Lutheran Confessions, as contained in the Book of Concord of 1580, something to which the congregation, Lutheran pastors, and our synod subscribes without reservation, also notes that the definition of a sacrament is not something to be quibbled over.  They say, “For no prudent man will strive greatly concerning the number or the term, if only those objects still be retained which have God's command and promises.”  The reason the Roman Catholic Church lists seven sacraments and we do not is because we don’t use the same definition.  The Apology of the Augsburg Confession, one of our Lutheran Confessions, says in Article XIII:

3] If we call Sacraments rites which have the command of God, and to which the promise of grace has been added, it is easy to decide what are properly Sacraments. For rites instituted by men will not in this way be Sacraments properly so called. For it does not belong to human authority to promise grace. Therefore signs instituted without God's command are not sure signs of grace, even though they perhaps instruct the rude [children or the uncultivated], or admonish as to something [as a painted cross]. 4] Therefore Baptism, the Lord's Supper, and Absolution, which is the Sacrament of Repentance, are truly Sacraments. For these rites have God's command and the promise of grace, which is peculiar to the New Testament. For when we are baptized, when we eat the Lord's body, when we are absolved, our hearts must be firmly assured that God truly forgives us 5] for Christ's sake. And God, at the same time, by the Word and by the rite, moves hearts to believe and conceive faith, just as Paul says, Rom. 10, 17: Faith cometh by hearing. But just as the Word enters the ear in order to strike our heart, so the rite itself strikes the eye, in order to move the heart. The effect of the Word and of the rite is the same, as it has been well said by Augustine that a Sacrament is a visible word, because the rite is received by the eyes, and is, as it were, a picture of the Word, signifying the same thing as the Word. Therefore the effect of both is the same.

Similarly in the Large Catechism, also part of the Book of Concord, Martin Luther writes:

74] And here you see that Baptism, both in its power and signification, comprehends also the third Sacrament [absolution], which has been called repentance, 75] as it is really nothing else than Baptism.

Absolution is a means of grace along with the preached Word, Baptism, the Lord’s Supper, and the mutual conversation and consolation of the brethren (Christians speaking God’s Word to each other).   In the 1991 synodical explanation to the Small Catechism also reminds us that while usually we speak of there being two sacraments, it is also acceptable, though not often mentioned, for Lutherans to speak of absolution as a third sacrament.  This is also stated in “What About Confession and Absolution,” in the popular tract series authored by the late Rev. Dr. A.L. Barry, former president of the LCMS.  So in conclusion, absolution “may” be freely referred to as a third sacrament among Lutherans, acknowledging that it is a “stretch” of the usual definition.   So as our confessions remind us, we will not “strive greatly about the number or term.”   In Scripture “sacrament” (mysterion – Greek) means “mystery” but beyond this it is a humanly-devised definition that is descriptive of what we find in the particulars of the means of grace.  The number of sacraments is an area of some flexibility according to the definition in our own official Confessions since 1580.