All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Actually we have not come across any authentic Hadith that states that learning Arabic is compulsory. Yet, one can induce from a general reading of the Shariah (Islamic law) evidences that some of the prominent companions of the Prophet urged Muslims imperatively to learn Arabic. In 'Shu'ab El-Eman' [branches of faith], Al-Baihaqi narrated that Umar Ibn Al-Khattab said: Learn Arabic for it strengthens the mind and enhances chivalry. It is narrated in the 'Musannaf" of Ibn Abi Shaibah that Umar also wrote to Abu Musa al-Ash'ari: Learn the Sunnah (Prophet's Tradition) and Arabic. Learn to parse the Qur'an for it is written in Arabic. In another version, he said: learn Arabic for it is part and parcel of your Religion. It is also narrated in the aforementioned 'Musannaf' that Ubayy Ibn Ka'b said: Learn Arabic as you learn (memorize) the Qur'an. Learning Arabic is of two types: individual obligation (that must be done by every individual) and communal (group) obligation (that must be done by a certain group of people). Examples of the individual obligation are learning the Surah al-Fatihah (the first chapter of the Qur'an), Tashahhud in the prayers (part of the prayer where one reads while sitting), and all other conditions without which a prayer is not valid. An example of the communal obligation is learning Arabic and teaching it to others. Sheikh-ul-Islam Ibn Taymiyah said: It is well known that learning Arabic and teaching it is one of the communal obligations. The Salaf (our righteous predecessors) used to punish their children for committing linguistic mistakes. So it is highly recommended that we preserve the Arabic linguistic rules and amend the diverse tongues (that fall short of following them) in a way that we preserve and maintain the Qur'an and Sunnah… . He also said: Umar 's instruction to learn Arabic helps in getting access to the knowledge of all aspects of the Deen (religion) for it (religion) comprises the knowledge of sayings and the knowledge of actions. Learning Arabic in the proper way leads to the knowledge of the Prophet's sayings, and the knowledge of Sunnah in the proper way leads to the knowledge of the Prophet's actions.
Allah knows best.