I highly doubt you will be asked this question. But it is true that interviews are conducted during office hours. That means if you are employed, then you will have to have a reason for not working. There are a couple of options. If the interview is less than two hours, you can schedule one during lunch time. If so, you can say you told your boss that you had to take care of some personal matters and you are taking an extended lunch. Another option is to tell the interviewer that your boss is aware of your interview schedule. But make sure it is true. I don't know what the best way to answer this question. But if I had to respond to this question, I would answer by saying I'm taking a personal day, or a vacation day. But make sure you don't say you are using a sick day. That is a complete lie and the interviewer will see that you are willing to lie for your personal gain.
This answer is turning an awkward question into an opportunity to show enthusiasm for the interview and the company. This is a key example where little things count. By adding the last sentence, the interviewer is sure to remember your answer more. That is because he or she will see your enthusiasm and excitement. If all the answers are the same, this one will be sure to stand out. When interviewing, everyone has similar answers. The key is to find opportunities to put in little extra comments to give you the advantage.