Shab -E- Meraj, as a physical journey, is established by the Holy Quran. Allah Ta’ala says:
Holy (free of any imperfection, weakness and insufficiency) is He Who took His (most beloved and intimate) Servant in a small portion of a night from the Sacred Mosque to the Al-Aqsa Mosque, whose surroundings We have blessed, in order that We might show him (the Perfect Servant) Our Signs. Surely He is the One Who is All-Hearing, All-Seeing. Surah Bani Israil (17:1)
The clearest proof that Meraj was a physical journey is the word ‘Abdihi. The Mufassirin (experts in interpretation of the Holy Quran) say about this that the soul and body together are called ‘Abd (Lit. slave). It is not given to only the soul or only the body. This shows that Meraj was physical journey, with both, the blessed body of the Holy Prophet Mohammed (Sallallahu alaihi wa sallam) and His blessed soul. As given in Tafseer Razi, Surah Bani Israil-1.
Burraq is also mentioned in the Sahih (rigorously-authenticated) Hadith. (Sahih Muslim, Hadith No. 429; Al Mustadrak Alas Sahihain Lil Hakim, Hadith No. 8946; Tahzeeb Ul Aathaar Lit Tabari, Hadith No. 2771; Mustakhraj Abi ‘Awana, Hadith No. 259; Musnab Abi Ya’ala, Hadith No. 3281; Muskhil Ul Aathaar Lit Tahawi, Hadith No. 4377; Jame’ Ul Ahadith, Hadith No. 553; Musnad Imam Ahmed, Hadith No. 12841; Majma Uz Zawaaid Wa Mamba ‘Ul Fawaid, Hadith No. 237). Obviously, a mount like Burraq is for the blessed body and not for the blessed soul.
Hadhrat Mulla Jivan (May Allah shower His mercy on him) writes about the journey of Meraj in Tafseeraat Ahmadiya:
Translation: The most authoritative opinion about Meraj is that it occurred in a wakeful state, for both the blessed body and the soul. This is the position of the Ahle Sunnah Wal Jama’ah. Therefore, the person who says that Meraj is only for the body or while sleeping, is an innovator in religion (Bida’ati), misguided, one who misguides and is out of the fold of obedience. (Tafseeraat Ahmadiya, Pg. No. 330)
Hadhrat Mulla Jivan (May Allah shower His mercy on him) also writes:
Translation: For this reason, the whole Ahle Sunnah Wal Jama’ah agrees that the journey of Meraj from Bait Ul Muqaddis is established by the Holy Quran and the journey of the heavens is established by Hadith Mashoor (i.e. a chain of narration (Sanad) in which in every era after the Sahabah, 3 or more than 3 persons report that Hadith) and beyond the seventh heaven is established by Khabr Wahid (a chain of narration in which in every era after the Sahabah, 1 person reports that Hadith). Thus, the person who denies/rejects the journey up till Masjid Aqsa from Masjid Haraam is a straightforward disbeliever, the person who denies the journey of the heavens is a Bid’ati and misguides others (innovator) and the person who denies the journey beyond the seven heavens is a sinner (Fasiq, Fajir). (Tafseeraat Ahmadiya, Pg. No. 328)
Sahih Bukhari Volume 007, Book 069, Hadith Number 482
Narrated By Abu Huraira : On the night Allah’s Apostle was taken on a night journey (Miraj) two cups, one containing wine and the other milk, were presented to him at Jerusalem. He looked at it and took the cup of milk. Gabriel said, “Praise be to Allah Who guided you to Al-Fitra (the right path); if you had taken (the cup of) wine, your nation would have gone astray.”