Rajab is one of the four sacred months that are mentioned in the Quraan.

Allaah Almighty states in the Holy Quraan

اِنَّ عِدَّۃَ الشُّہُوْرِ عِنْدَ اللّٰہِ اِثْنَا عَشَرَ شَھْرًا فِیْ کِتٰبِ اللّٰہِ یَوْمَ خَلَقَ السَّمٰوٰتِ وَ الْاَرْضِ مِنْھَا اَرْبَعَۃٌ حُرُمٌ ط ذٰلِکَ

الدِّیْنُ الْقَیِّمُ فَلَا تُظْلِمُوْا فِیْھِنَّ اَنْفُسِکُمْ (پارہ ١٠، سورہ توبہ، آیت ٣٦)

“Indeed the number of months before Allaah [Ta’aalaa] is twelve – in the Book of Allaah – since the day He created the heavens and the earth, of which four are sacred; this is the straight religion; so do not wrong yourselves in those months.” (Chapter 10, Soorah Taubaah, Verse 36)