In short, I believe it depends on your heart.
There is nothing intrinsically wrong with martial arts any more than aerobics, jogging, cycling, etc. If however, one performs martial arts as an act of worship, adoration, or dependence upon a false god or pagan force, then it becomes idolatrous, just as cycling becomes idolatrous if you "tap into the force" to go that extra mile. The exercise is not wrong, but the belief in a false god and dependence upon it is sin. The exercise serves merely the occasion for the sin, but is not sinful in and of itself. In fact, exercise is a wholesome thing, although of relatively minor benefit (I Timothy 4:8).
Meditation is slightly different in that it is more commonly associated with spiritual things. However, that is not a necessary relation. An atheist may "meditate" in his office at work about business strategy, solving technical problems, resolving personal relationships, etc., but never flex a spiritual muscle. That being said, meditation associated with martial arts may indeed have a spiritual connotation. Therefore, like martial arts, meditation may become sin, depending upon a person's heart and their purpose for meditation.
Again, meditation is not intrinsically wrong. In fact, "pondering" and "meditation" are invaluable tools in the Christian's walk, especially if they involve self-examination (II Corinthians 13:5). Try using the side-bar to look up all forms of meditation in the Bible (meditat*). The Psalms are filled with positive references to meditation. In contrast to this, Proverbs speaks foreboding words for those who refuse to ponder their own ways before the Lord (Proverbs 4:26; 5:21).
Admittedly, I have enjoyed and benefited physically from my past experience in martial arts. In combination with swimming and weight training, I consider it to be the ultimate regimen for physical exercise. ... At 2 of the schools I visited, our teacher would dedicate a quiet minute to meditation at the beginning and end of each class. I always spent the time in prayer, thanking God for the day and my health. I would ask him to bless the activities of that hour to the welfare of my physical body. Finally, I would pray that the Lord would help me to maintain the appropriate place for these activities, emphasizing spiritual growth and welfare in His Word above all these physical activities (I Timothy 4:8). As I grew older, I spent less time in such activities, because I grew into much better ways to spend my allotted time in the Lord's service. In fact, I now spend barely any time exercising - just enough so that my body does not fail me prematurely, but no more.
In conclusion, both of these activities are perfectly innocent in and of themselves. However, if one uses these activities as a means to tap into an idolatrous force or being, then it becomes sin for such a person (I Corinthians 6:9-10)