What is the ruling on a man who divorced his wife and then married another woman seven days after his divorce?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

It is permissible for a man who divorced his wife to marry another woman under two conditions:

1.     If the husband divorced his wife with a revocable divorce, the new wife should not be his ex-wife’s paternal aunt, sister, or maternal aunt; since it is forbidden for Muslim men to marry a woman and her paternal aunt, sister, or maternal aunt simultaneously. Abu Hurayrah narrated that the Prophet, sallallaahu ‘alayhi wa sallam, said: “The woman and her paternal aunt should not be married to the same man (at the same time); and similarly, the woman and her maternal aunt should not be married to the same man (at the same time).” [Al-Bukhari and Muslim]

Moreover, Allaah The Exalted Says (what means): {…And that you take [in marriage] two sisters simultaneously.} [Quran 4:23]

This is the case if the divorce was revocable and the ‘Iddah, i.e. post-marriage waiting period, was not yet over; since his ex-wife would still be regarded as his wife during her ‘Iddah.

2.     That it wasn't his fourth wife, which he divorced with a revocable divorce and the ‘Iddah was not yet over, in this case, if he married another wife during the ‘Iddah, he would be married to five wives which is forbidden in Islam according to all scholars.  Allaah The Exalted also Says (what means): {And if you fear that you will not deal justly with the orphan girls, then marry those that please you of [other] women, two or three or four. But if you fear that you will not be just, then [marry only] one or those that your right hand possesses. That is more suitable that you may not incline [to injustice].} [Quran 4:3]

Allaah Knows best.