Why is the week seven days?

Firstly: 

We cannot be certain about anything with regard of the division of the week into seven days, or the time when this division began – was it before the creation of the heavens and the earth, or was the creation of the heavens and the earth what led to this division? The reason for that is that we have no clear evidence which states anything certain to that effect. But what is indicated by a study of calendars and the customs and reports of different nations is that the division of the week into seven days is connected to religion and taken from it, and that it has to do with reports and rulings of religion. 

Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) said in Majmoo’ al-Fataawa (7/95): 

Every nation that does not have a Book has no names for days of the week in their languages, rather they have names for the day, the month and the year, because that may be known on tangible and rational ways, so the nations gave them names, because expression follows visualization. But the week was only known by hearing (reports). It was not known that Allaah created the heavens and the earth and everything in between in six days then rose over the Throne except by the words of the Prophets who were enjoined to gather together on one day of the week to worship Allaah and remember the first week in which Allaah began to create the universe. In Arabic and Hebrew and the languages of those who learned from them, there are words for the days of the week, unlike the language of the Turks and others like them; there are no words for the days of the week in their language because they did not know of that so they have no words for it. 

Dr. Jawaad ‘Ali says: 

The month is divided into four sections, and each section is a week composed of seven days. 

The idea of this division is attributed to the Babylonians, but the days of the week and their order in the manner that is known until now is a system that appeared long after them. The week (shavu’ah in Hebrew) is mentioned in the Torah, in the Book of Genesis. Based on both the Jewish Sabbath and the story of creation, the week was organized along the lines that are still prevalent today. End quote. 

Al-Mufassal fi Tareekh al-‘Arab qabl al-Islam (16/96). 

And Allaah knows best.