Objection 1. It seems that fear is not a sin. For fear is a passion, as stated above (I-II, 23, 4; 42). Now we are neither praised nor blamed for passions, as stated in Ethic. ii. Since then every sin is blameworthy, it seems that fear is not a sin.
Objection 2. Further, nothing that is commanded in the Divine Law is a sin: since the "law of the Lord is unspotted" (Psalm 18:8). Yet fear is commanded in God's law, for it is written (Ephesians 6:5): "Servants, be obedient to them that are your lords according to the flesh, with fear and trembling." Therefore fear is not a sin.
Objection 3. Further, nothing that is naturally in man is a sin, for sin is contrary to nature according to Damascene (De Fide Orth. iii). Now fear is natural to man: wherefore the Philosopher says (Ethic. iii, 7) that "a man would be insane or insensible to pain, if nothing, not even earthquakes nor deluges, inspired him with fear." Therefore fear is not a sin..
On the contrary, our Lord said (Matthew 10:28): "Fear ye not them that kill the body," and it is written (Ezekiel 2:6): "Fear not, neither be thou afraid of their words."
I answer that, A human act is said to be a sin on account of its being inordinate, because the good of a human act consists in order, as stated above (109, 2; 114, 1). Now this due order requires that the appetite be subject to the ruling of reason. And reason dictates that certain things should be shunned and some sought after. Among things to be shunned, it dictates that some are to be shunned more than others; and among things to be sought after, that some are to be sought after more than others. Moreover, the more a good is to be sought after, the more is the opposite evil to be shunned. The result is that reason dictates that certain goods are to be sought after more than certain evils are to be avoided. Accordingly when the appetite shuns what the reason dictates that we should endure rather than forfeit others that we should rather seek for, fear is inordinate and sinful. On the other hand, when the appetite fears so as to shun what reason requires to be shunned, the appetite is neither inordinate nor sinful.
Reply to Objection 1. Fear in its generic acceptation denotes avoidance in general. Hence in this way it does not include the notion of good or evil: and the same applies to every other passion. Wherefore the Philosopher says that passions call for neither praise nor blame, because, to wit, we neither praise nor blame those who are angry or afraid, but only those who behave thus in an ordinate or inordinate manner.
Reply to Objection 2. The fear which the Apostle inculcates is in accordance with reason, namely that servants should fear lest they be lacking in the service they owe their masters.
Reply to Objection 3. Reason dictates that we should shun the evils that we cannot withstand, and the endurance of which profits us nothing. Hence there is no sin in fearing them.
Source: Summa Theologica (New Advent)