Can my husband marry my niece i.e. my sister's daughter?

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.

It is not permissible for your husband to marry your sister's daughter (niece). It is forbidden for him to combine the two of you according to the Hadeeth reported by Al-Bukhaari and Muslim. Abu Hurayrah narrated that the Prophet forbade combining between a woman and her paternal aunt, and between a woman and her maternal aunt. [This wording is Muslim’s]

An-Nawawi said in his explanation of Saheeh Muslim:

"Another narration reads as follows: 'A paternal aunt should not be combined with her brother's daughter, nor the daughter of a sister with her maternal aunt.' this is the proof of the view of all the scholars that it is forbidden to combine between a woman and her paternal aunt and between her and her maternal aunt.” [End of quote]

Ash-Sharh Al-Mumti’ by Shaykh Ibn 'Uthaymeen reads:

“The women who are forbidden to be combined in marriage are of three categories: 'Two sisters; the paternal aunt and the daughter of her brother; the maternal aunt and the daughter of her sister.'" [End of quote]

For more benefit, please refer to Fataawa 85322, 85868 and 330067.

Allah knows best.