A woman who is menstruating may do all acts of worship apart from praying, fasting, circumambulating the Ka'bah and doing i'tikaaf in the mosque.
It was narrated that the Prophet (peace and blessings of Allaah be upon him) used to stay up at night during the last ten nights of Ramadaan. Al-Bukhaari (2401) and Muslim (1174) narrated that Aa'ishah (may Allaah be pleased with her) said: When the last ten nights of Ramadaan came, the Prophet (peace and blessings of Allaah be upon him) would refrain from marital relations, stay up at night and wake his family up.
Staying up at night is not only for prayer, rather it includes all kinds of acts of worship. This is how the scholars interpreted it.
Al-Haafiz said: Staying up at night means staying up to do acts of worship.
Al-Nawawi said: spending the night staying up to pray etc.
He said in Awn al-Ma'bood: i.e., in prayer, dhikr and reciting the Qur'aan.
Praying qiyaam is the best act of worship that a person can do on Laylat al-Qadr. Hence the Prophet (peace and blessings of Allaah be upon him) said: Whoever spends the night of Laylat al-Qadr in prayer out of faith and in hope of reward, his previous sins will be forgiven. (Narrated by al-Bukhaari, 1901; Muslim, 760).
Because the woman who is menstruating is not allowed to pray, she can spend the night in doing other acts of worship apart from prayer, such as:
1- Reading or reciting Qur'aan. See question no. 2564.
2- Dhikr - such as saying Subhaan-Allaah, La ilaaha illa-Allaah, al-Hamdu Lillaah, etc. She can repeat the words Subhaan-Allaah wa'l-hamdu Lillaah, wa laa ilaaha ill-Allaah, wa Allaahu akbar (Glory be to Allaah, praise be to Allaah, there is no god but Allaah and Allaah is Most Great) and Subhaan Allaah wa bi hamdihi, subhaan Allaah il-Azeem (Glory and praise be to Allaah, glory be to Allaah the Almighty) etc.
3- Istighfaar (praying for forgiveness), by repeating the phrase Astaghfir-Allaah (I ask Allaah for forgiveness).
4- Du'aa' (supplication) - she can pray to Allaah and ask Him for what is good in this world and in the Hereafter, for du'aa' is one of the best acts of worship. The Prophet (peace and blessings of Allaah be upon him) said, Du'aa' is ibaadah (worship). (Narrated by al-Tirmidhi, 2895; classed as saheeh by al-Albaani in Saheeh al-Tirmidhi, 2370).
The woman who is menstruating can do these acts of worship and others on Laylat al-Qadr.
We ask Allaah to help us to do that which He loves and which pleases Him. May Allaah accept our righteous deeds.
Reproduced from Islam QA