The Holy Quran mentions about the Racism: O mankind! Indeed, We created you from a male and a female and made you nations and tribes that you may identify yourselves with one another. Indeed, the noblest of you in the sight of Allah is the most God wary among you. Indeed, Allah is all-knowing, all-aware (49:13).

"The issue of equality between all human beings, opposition to any type of racial, ancestral and class discrimination, fairness between all the children of Adam in relation to human rights and that no person is better than another due to his skin color, language, lineage or race - is one of the most important societal issues in the Qur’an which has been mentioned in various verses of this Heavenly Book. The Qur’an has denounced all sorts of superiority - whether it be of race, language, or skin color." 

Likewise, Prophet Muhammad (PBUH & HP) says: Surely all of mankind – from the time of Adam until our time – are like the teeth of a comb (all equal to one another) and there is no greatness for an `Arab over a non-`Arab and no greatness for a red-skinned person over a black-skinned person, except due to one’s consciousness of Allah (taqwa).”

There are numerous verses in the Holy Quran and the teachings of the Holy Prophet (PBUH & HP) that invite human beings towards brotherhood and equality. Throughout his life, the Holy Prophet (PBUH & HP) taught people that all humans are one and the only difference that exists is in their God-wariness as mentioned in verse 13 of Surah Hujarat. We learn from the Holy Prophet (PBUH & HP) and the Ahlul Bayt (AS) that Islam has established equality for the entire human race and struck at the very root of all distinctions based on color, race, language or nationality. According to Islam, Allah has given man this right of equality as a birthright. Thus, no man should be discriminated against on the basis of the color of his skin, his place of birth, his race or the nation in which he was born. 

Apart from conveying the pure teachings of Islam, the Holy Prophet (PBUH &HP) was also able to rouse hope in the hearts of the poor and the downtrodden section of his society. In many instances within his practical life, he was successful in eliminating bigotry and racism that was surrounding him. In order for him to reach his aim of equality between all human beings, he married the daughter of his uncle to a slave named Zaid. In addition, he gave Bilal, who was both a non-`Arab and an African slave (at one point in his life), the important religious post of being the Muaddhin, the one who calls to prayer. He also convinced Ziyad ibn Labid who was one of the richest and noblest men from amongst the Ansar to marry his daughter to an African slave named Jubair. This marriage between a nobleman's daughter and a slave, was the beginning of many such marriages that broke mental and social barriers among the followers of Islam. Islam is a practical example of how human beings and societies can fight racial discrimination and create a society based on unity and brotherhood.

Martyr Malcolm X Talks about Racism in Hajj

The annual ritual of Hajj is an outstanding display of beauty and splendor among the followers of Islam and it is this very beauty of Islam that inspired (Martyr) Malcolm X to write the following letter after he made his first Hajj:

"Never have I witnessed such sincere hospitality and overwhelming spirit of true brotherhood as is practiced by people of all colors and races here in this ancient Holy Land, the home of Abraham, Muhammad and all the other prophets of the Holy Scriptures. For the past week, I have been utterly speechless and spellbound by the graciousness I see displayed all around me by people of all colors.....There were tens of thousands of pilgrims, from all over the world. They were of all colors, from blue-eyed blondes to black-skinned Africans. But we were all participating in the same ritual, displaying a spirit of unity and brotherhood that my experiences in America had led me to believe never could exist between the white and the non-white. You may be shocked by these words coming from me. But on this pilgrimage, what I have seen, and experienced, has forced me to rearrange much of my thought-patterns previously held, and to toss aside some of my previous conclusions. This was not too difficult for me. Despite my firm convictions, I have been always a man who tries to face facts, and to accept the reality of life as new experience and new knowledge unfolds it. I have always kept an open mind, which is necessary to the flexibility that must go hand in hand with every form of intelligent search for truth.
During the past eleven days here in the Muslim world, I have eaten from the same plate, drunk from the same glass and slept in the same bed (or on the same rug)-while praying to the same Allah with fellow Muslims, whose eyes were the bluest of the blue, whose hair was the blondest of blond, and whose skin was the whitest of white. And in the words and in the actions and in the deeds of the ‘white' Muslims, I felt the same sincerity that I felt among the black African Muslims of Nigeria, Sudan and Ghana.
We are truly all the same-brothers.
All praise is due to Allah, the Lord of the worlds."

Conclusion:

The Holy Quran tells us:
"Certainly, We have honored the Children of Adam, and carried them over land and sea, and provided them with all the good things, and preferred them with a complete preference over many of those We have created." (17:70)

The Holy Quran teaches us that Islam lays down some rights for man as a human being. Every man whether he belongs to one country or the other, whether he is a believer or a non-believer, whether he lives in forest or desert, whatever be the case, he has some basic human rights simply because he is a human being, which should be recognized by every human being.

Today, the world is struggling to come to terms with equality in true sense. Racial discrimination continues to be a challenge, even for the most developed nations. However, Islam has shown the way to fight racial discrimination and create a society based on amity, love and unity. InshaAllah, the world will very soon realize that the only solution to racism lies in following Islam.

References:
1. Islamic Moral System: Commentary of Surah Al-Hujurat Ayt. Jafar Subhani
2. Malcolm X's letter http://islam.uga.edu/malcomx.html