A woman and her husband are not allowed to have vaginal intercourse during her menses. This is haram according to the consensus of Scholars and the text of the Quran.
However, they may engage in physical intimacy through kissing, hugging, and touching areas above the wife's navel and below her knee. Scholars have differed on whether intimacy is permissible in the area between the navel and the knee, excluding the front or back passage. Note that anal penetration is always prohibited in Islam, both during menstruation and outside of it, with only vaginal penetration being permissible.
Muslim narrated from Anas that the Jews, if any of their women were menstruating, would not eat with them or meet with them in their houses. The Companions of the Prophet (Salla Allahu 'Alayhi Wa Sallam) asked Him about that, then Allah revealed the verse (interpretation of the meaning):
"They ask you concerning menstruation. Say: that is an adha (a harmful thing for a husband to have a sexual intercourse with his wife while she is having her menses), therefore, keep away from women during menses and go not unto them till they are purified (from menses and have taken a bath). And when they have purified themselves, then go in unto them as Allah has ordained for you (go in unto them in any manner as long as it is in their vagina). Truly, Allah loves those who turn unto Him in repentance and loves those who purify themselves." [Al-Baqarah 2:222].
The Messenger of Allah (Salla Allahu 'Alayhi Wa Sallam) said: "So do everything except intercourse." News of that reached the Jews and they said, "What does this man want? He does not leave any of our affairs but he differs from it!"
In this verse, "keep away" means refraining from having sexual relations with one's wife during her menstruation, while going unto them refers to the resumption of intimacy after she has purified herself, meaning after the end of her menstruation and the completion of Ghusl (ritual purification).
Also, the term "Fi'l-mahid" (translated as "during menses") refers to both the period of menstruation and the location of menstruation, specifically the vagina.
The scholars that saw that it is permissible to engage in intimacy between the navel and below her knee, other than sexual intercourse, argued that the fact that the site of bleeding is mentioned specifically in the verse of the Quran, and the fact that the Prophet (Salla Allahu 'Alayhi Wa Sallam) said: "So do everything except intercourse." indicate that it is permissible to be intimate in other areas without exceptions. Imam Ahmad Ibn Hanbal was of the view that this is permissible, as well as some Hanafis, Malikis and Shafi`is.
On the other side, other scholars such as Imam Abu Hanifah, Imam Malik and al-Shafi`i were of the view that it is not permissible to engage in intimacy in the area between the navel and the knee. One of the evidence behind this opinion is derived from the hadith of 'Aishah narrated by Al-Bukhari and Muslim, who said: "If one of us was menstruating and the Messenger of Allah (Salla Allahu 'Alayhi Wa Sallam) wanted to be intimate with her, he would tell her to wear an Izar (waist wrapper) at the peak of her menstruation, then he would be intimate with her."
Ibn al-Qayyim did not see a contradiction between the hadiths about the Izar and the first opinion; he did not considered the Prophet's action and use of the Izar as a recommendation and a precautionary measure, rather than an indication of prohibition.