Not to be pedantic, but you're referring to Hadith 6960 from the Sahih Muslim, which is one of the Hadith books, not the Qur'an. The difference is that the Ahadith are indirect quotations of Muhammad, as related by a chain of narrators (some considered strong, others weak). Sahih Bukhari and Sahih Muslim are considered to be the two most reliable ones by Sunni Muslims. However, the veracity of many hadiths is assailable, because there tend to be holes in the narration links, and some hadith are contradictory.

This hadith is also found in Sahih Bukhari. It is most likely not in reference to the Mongols, but rather Turkic peoples. Bukhari and Muslim were both collected long after Muhammad's death, well into the reign of the Abbasid Caliphate. This would have been around the time when Turks, prior to their conversion to Islam, would have begun migrations and invasions into Muslim territories in Central Asia, and Persia. Muhammad al-Bukhari, the man who compiled the Sahih Bukhari, was from Central Asia, beginning and ending his life and studies in the region (although he traveled widely through the Abbasid caliphate). That immediately calls into question whether or not this hadith, attributed to Prophet Muhammad, is a product of Bukhari's geopolitical surroundings.