The Prophet (peace and blessings be upon him) said, “Islam is built upon five pillars: testifying that there is no true god except Allah and that Muhammad is the Messenger of Allah, performing Prayer, paying the Zakah, making the pilgrimage to the Sacred House (Hajj), and fasting the month of Ramadan.” (Reported by Al-Bukhari).
Regarding this issue, Sheikh `Atiyyah Saqr, states:
“Allah says in the Qur’an, “They ask you concerning the new moons. Say: They are but signs to mark fixed periods of time. In the affairs of men, and for Pilgrimage.” (Al-Baqarah: 189). Also, He, Most High, says, “for Hajj are the months well-known. If any one undertakes that duty therein, let there be no obscenity, nor wickedness, nor wrangling in the Hajj. And whatever good you do, be sure Allah knows it.” (Al-Baqarah: 197).
Hajj is an Islamic ritual like prayer (salat) and fasting which should be carried out at a specified period of time.
As for the months of Hajj, they are; Shawwal, Dhul-Qi`dah, and Dhul-Hijjah. Henece, If a person makes Ihram (i.e., a sacred state which a Muslim must enter in order to perform the major Hajj) before Shawwal, his Hajj is incorrect according to Ibn `Abbas, Ibn `Umar, and Ash-Shafi`i.
Conversely, Abu Hanifah, Malik, and Ahmad see that the Ihram is correct but that is not recommended. But as for the `Umrah, there is no specified time for it.”