Singing by women is not specifically mentioned by the Qur'an.
However, verses 31:6 and 23:3 are often interpreted to refer to a prohibition on music, or certain types of music, due to the use of the words lughw and lahw (vain or idle speech).
In Surat al-Ahzab, there are also instructions to the Prophet's wives telling them to speak "plainly".
Hope that helps!