Although I find no place in the Bible that commands daughters to follow the will of their fathers in marriage, it seems to be assumed throughout the Bible that this is the case. The question is whether this is a direct command for today or whether it is only an honored custom of Bible times that is still followed in older cultures in the world today. I think it would be wise to look at some of the passages and then to try to draw some sane conclusions from them.
In the Bible, daughters are given to the sons of others but are taken from their parents for one's own sons.
Genesis 34:9 states, "And make ye marriages with us, and give your daughters unto us, and take our daughters unto you."
Deuteronomy 7:3 warns against marriage with the heathen with these words: "Neither shalt thou make marriages with them; thy daughter thou shalt not give unto his son, nor his daughter shalt thou take unto thy son."
Similar wording is found in other places. The daughters were either given to the son of another family or were taken from another family for one's own son.
In the New Testament, we have this passage:
1 Corinthians 7:36-38 But if any man think that he behaveth himself uncomely toward his virgin, if she pass the flower of her age, and need so require, let him do what he will, he sinneth not: let them marry. Nevertheless he that standeth stedfast in his heart, having no necessity, but hath power over his own will, and hath so decreed in his heart that he will keep his virgin, doeth well. So then he that giveth her in marriage doeth well; but he that giveth her not in marriage doeth better.
Some interpret this as referring to a man's behavior toward the one he wants to marry. However, verse 38 shows that this passage is referring to a father giving his daughter in marriage. The desire of a father that his daughter marry was strong in Bible times. Paul was advising against marriages because of the persecution the Christians were then facing. He was not speaking against marriage for all times. He was not even forbidding it in times of persecution. His advice was in the context of this phrase: "I suppose therefore that this is good for the present distress" (1 Corinthians 7:26). He was not advocating perpetual virginity for all times.
The question is, Where do we go with this information? It is clear that daughters were given in marriage by the fathers. Evidently, it was considered important to watch over them in order to protect and to guide them in their choice of a husband. However, although children (both sons and daughters) are commanded to honor and obey their parents, there does not seem to be a command anywhere in scripture that daughters must in all cases follow the will of the father. I, for one, have certainly seen this practice misused. In America there are those who teach their children at home (we did this with our children). Some homeschooling groups have emphasized the importance of the parents controlling the marriage decisions of their children. Unfortunately, some have taken this way overboard. I have known fathers to give applications of many pages long to prospective son-in-laws. I have also seen them try to force the young man to jump through various hoops in order to prove himself worthy of the daughter. Some of the demands have been so humiliating that the father is actually asking the young man to fail to be much of a man in order to marry his daughter. This is not right.
Here is my conclusion. It is important for the father to be a strong part of his daughter's decision in marriage. He should guide her and warn her of things he sees that she may not understand. If he refuses to give his blessing on the marriage and he has developed a close relationship with his daughter over the years, it might keep her from falling a trap of the devil. However, this is not an ownership type of control. Fathers are not to lord over their daughters and their future. They should work together to seek the will of the Lord. Now, if the culture has a practice of the parents arranging the marriage of the children, that is fine. This is certainly the normal practice in scripture. However, if it is not a part of the culture, then a softer approach should be taken. The father should lead, but not dictate absolutely. Only if he clearly sees danger ahead should he refuse to give his blessing. Then, if the daughter marries anyway (as is often the case), he should love her and her family even though they married against his will.