The Old Testament Law commanded the Israelites not to engage in interracial marriage (Deuteronomy 7:3-4). However, the reason for this was not primarily racial in nature. Rather, it was religious. The reason God commanded against interracial marriage was that people of other races were idolaters and worshippers of false gods. The Israelites would be led astray from God if they intermarried with idol worshippers, pagans, or heathens. A similar principle is laid out in the New Testament, but at a much different level: “Do not be yoked together with unbelievers. For what do righteousness and wickedness have in common? Or what fellowship can light have with darkness?” (2 Corinthians 6:14). Just as the Israelites (believers in the one true God) were commanded not to marry idolaters, so Christians (believers in the one true God) are commanded not to marry unbelievers. To answer this question specifically, no, the Bible does not say that interracial marriage is wrong.
As Martin Luther King noted, a person should be judged by his or her character, not by skin color. There is no place in the life of the Christian for favoritism based on race (James 2:1-10). When selecting a mate, a Christian should always first find out if the potential spouse is born again by faith in Jesus Christ (John 3:3-5). Faith in Christ, not skin color, is the biblical standard for choosing a spouse. Interracial marriage is not a matter of right or wrong, but of wisdom, discernment, and prayer.
The only reason interracial marriage should be considered carefully is the difficulties a mixed-race couple may experience because of others who have a hard time accepting them. Many interracial couples experience discrimination and ridicule, sometimes even from their own families. Some interracial couples experience difficulties when their children have skin tones of different shades from the parents and/or siblings. An interracial couple needs to take these things into consideration and be prepared for them, should they decide to marry. Again, though, the only biblical restriction placed on whom a Christian may marry is whether the other person is a member of the body of Christ.