Islam urges its followers to marry as soon as possible as long as they are financially and physically able. Marriage in Islam is both a religious ordinance as well as a Prophetic Sunnah. What has been circulated regarding marriage in the month of Muharram is a baseless claim that has no any religious backing.
Tackling the issue from a broader and wider dimension, Dr. Muzammil H. Siddiqi, former President of the Islamic Society of North America, states:
The Day of `Ashura’ (10th of Muharram) is certainly a sad day in the history of Islam. It was on this day that the grandson of the Prophet (i.e. Imam Al-Husayn, may Allah be pleased with him) along with many members of his family were brutally massacred in Karbela’ in the year 61 of Hijrah or 680 of the common era.
It is important to remember those tragic events and to derive lessons from them. It is also the Sunnah of the Prophet (peace and blessings be upon him) to fast on the 9th and 10th days of Muharram. The Prophet (peace and blessings be upon him) did fast on this day remembering Allah’s deliverance of Prophet Musa (peace and blessings be upon him) and his followers from the persecution and oppression under the Pharaoh of Egypt. However, besides fasting and remembering the tragic events of Imam Al-Husayn’s martyrdom, there is no other mourning required on these days.
There is nothing wrong in holding wedding ceremonies or any other parties on this day or in the month of Muharram as such. All days belong to Allah and Muslims should not take any superstitions from any months or days.