Islam teaches people to cooperate with one another in goodness and to help alleviate the calamities that afflict their brothers and sisters in humanity with all sorts of assistance and consolation.
Moreover, we should take into consideration that such universal phenomena are sings and indications of Allah’s majesty. Though they normally occur on scientific grounds, but we should not forget that the Ever-Wise Allah is the one Who sets such precise order for His creation, while finally He wants people to remember that they, no matter the scientific level they have reached, are still within His power and omnipotence.
Answering your question, Sheikh `Abdel-Khaliq Hasan Ash-Shareef, a renowned Azharite scholar, stated,
From an Islamic viewpoint, this momentous incident reflects Allah’s sovereignty and omnipotence, as He, the Almighty, inflicts these adversities on whom He wills, whenever He wills, and without recourse to anyone. There is none who can prevent His judgment, and He is Swift in reckoning. Such unavoidable incidents are to remind people that there is a mighty power that rules the universe, and people should resort to the owner of this power with worship and monotheism. They should remember that none but Allah deserves to be worshipped. Moreover, such agonizing incidents remind people of the Last Day, which they have been distracted from by the luxury of this life. Thus, they should be fearful of Allah’s punishment, which none is able to avert.
As for our duty and role, it should be known that all humanity, with all its sects, doctrines, ideologies, races, and colors, has a great responsibility toward the stricken community. It is obligatory on all humans to help the victims of this earthquake and provide them with various kinds of aid. They should offer as much assistance as possible, including food and medical, financial, and social aid.
There should not be any sense of indifference, because we are all descendants of Adam. Moreover, Prophet Muhammad (peace and blessings be upon him) said,
“In [t he benevolence offered] to every living creature, there is a reward.”(Al-Bukhari)
Also, Anas ibn Malik (may Allah be pleased with him) reported that the Messenger of Allah (peace and blessings be upon him) said,
“The Muslim who plants something and birds or people or animals eat from it will have this act as an act of charity.”(Al-Bukhari and Muslim)
All people on this globe should stand together to help those afflicted people, who have become subject to diseases, pains of hunger, and lack of daily rations and even the basic needs of human beings. We should assist them and rescue those who call us from between the ruins and from under the debris of demolished buildings.
It should be clear that people are equal, especially in these calamities, and no attention should be paid to the differences in cultures, religions, or races. If Muslims abstain from helping non-Muslims in distress or vise versa, then they would be held accountable before Allah on the Day of Resurrection.
Also, Dr. Hatem Al-Haj, dean of the Sharia Academy of America, added,
In Islam, it is advisable to give charity and help all needy people. Allah says,
(And [the righteous] feed with food the needy wretch, the orphan, and the prisoner, for love of Him.) (Al-Insan 76:8)
It is also known that the Prophet (peace and blessings be upon him) said,
“In [the benevolence offered] to every living creature, there is a reward.”(Al-Bukhari)
Moreover, the kind treatment of people afflicted with such disasters may be the best way to reconcile their hearts. That is not exploitive proselytizing, because you will not exploit them in any cheap way; you will help them out of a concern for humanity and keenness on their welfare.