Luther rejected the idea that one could be justified by works of the Law, but he also taught that Christians should obey the Ten Commandments. He makes this clear, for example in the Small Catechism.
With young persons keep to a single, fixed, and permanent form and
wording, and teach them first of all the Ten Commandments, the Creed,
the Lord’s Prayer, etc., according to the text, word for word, so that
they can repeat it after you and commit it to memory... After they
understand well the meaning of the First Commandment, proceed to the
Second, and so on, otherwise they will be too overwhelmed to the point
of remembering nothing.
... After you have so taught them this short catechism, take up the
Large Catechism and use it to give them a broader and richer
understanding. Here enlarge on every individual commandment, petition,
segment, explaining in each case the various words, uses, benefits,
dangers, and hurts involved, as you will find them amply described in
many a book dealing with these topics.
Like other Reformers, Luther saw obedience to the commandments not as a means of salvation but as manifestations of its fruits. From the Westminster Confession
Chapter 16:
Good works, done in obedience to God’s commandments, are the fruits
and evidences of a true and lively faith: and by them believers
manifest their thankfulness, strengthen their assurance, edify their
brethren, adorn the profession of the gospel, stop the mouths of the
adversaries, and glorify God, whose workmanship they are, created in
Christ Jesus thereunto, that, having their fruit unto holiness, they
may have the end, eternal life.
Chapter 19
God gave to Adam a law, as a covenant of works.. This law, after his
fall, continued to be a perfect rule of righteousness; and, as such,
was delivered by God upon Mount Sinai in ten commandments, and written
in two tables; the first four commandments containing our duty toward
God, and the other six our duty to man.
Although true believers be not under the law as a covenant of works,
to be thereby justified or condemned; yet is it of great use to them,
as well as to others; in that, as a rule of life, informing them of
the will of God and their duty, it directs and binds them to walk
accordingly; discovering also the sinful pollutions of their nature,
hearts, and lives; so as, examining themselves thereby, they may come
to further conviction of, humiliation for, and hatred against sin;
together with a clearer sight of the need they have of Christ, and the
perfection of His obedience.
Conclusion: Luther instructed his followers that the Ten Commandments should be taught and obeyed, even though believers are not "under the law" in terms of salvation.
ADDENDUM:
The OP has pointed out that in a letter {correction: sermon} titled "How Christians Should Regard Moses" Luther takes a rather dim view of the Mosaic Law, stating that it is definitely NOT binding on Christians. However, he also says: "I would take from Moses a model for statutes; not that Moses should be binding on me, but that I should be free to follow him in ruling as he ruled." Moreover, Luther does specifically affirm the Ten Commandments, which he says are part of what we would call natural law.
They say, “he has commanded that we should have one God, that we should trust and believe in him, that we should not swear by his name; that we should honor father and mother; not kill, steal, commit adultery; not bear false witness, and not covet [Exod. 20:3–17]; should we not keep these commandments?” ... Nature also has these laws. Nature provides that we should call upon God. The Gentiles attest to this fact...The Gentiles have it written in their heart, and there is no
distinction [Rom. 3:22]. As St. Paul also shows in Romans 2, the
Gentiles, who have no law, have the law written in their heart.
We should also recognize that this letter, written seemingly in haste in 1525, seems not to represent Luther's mature view. In 1529, in the Small Catechism - a carefully constructed formal document - he instructs pastors that the Commandments be diligently taught, especially to young people, placing them on a par with the Lord's Prayer and the Apostles Creed.