So far the Qur'an is concerned , there is no evidence of Prophet Muhammad's ascension to heaven which is traditionally called Isra or Mirajj.The verse that is believed to be associate with this is :
[017:001] Glory to (God) Who did take His servant for a Journey by night from the Sacred Mosque to the farthest Mosque, whose precincts We did bless,- in order that We might show him some of Our Signs: for He is the One Who heareth and seeth (all things).
This verse doesn't mention the name rather said 'His servant' .Now the question is who is this servant . Traditionally it is interpreted as Prophet Muhammad . But if you restrict yourself within the Qur'an , to look for the answer for this question , the immediate next verse will answer you that it was prophet Moses :
[017:002] And WE gave Moses the Book and WE made it a guidance for the Children of Israel, commanding, `Take ye no guardian beside ME,
If you keep on reading the verse 3,4,5... you will see that all are about Prophet Moses and his tribe Bani Israel . In fact the chapter itself named ' Bani Israel' which predicts the sura to be dedicated to discuss about the story of Moses and his tribe primarily .
Also it would be really appealing to inquire whether Prophet Moses had ever undertaken any night journey which might appear noticeable/vital for his life . Yes , we really do find this incident described by Almighty ALLAH in Qur'an in sevearl different places :
[028:029] Now when Moses had fulfilled the term, and was traveling with his family, he perceived a fire in the direction of Mount Tur. He said to his family: "Tarry ye; I perceive a fire; I hope to bring you from there some information, or a burning firebrand, that ye may warm yourselves."
[028:030] But when he came to the (fire), a voice was heard from the right bank of the valley, from a tree in hallowed ground: "O Moses! Verily I am God, the Lord of the Worlds....
[028:031] "Now do thou throw thy rod!" but when he saw it moving (of its own accord) as if it had been a snake, he turned back in retreat, and retraced not his steps: O Moses!" (It was said), "Draw near, and fear not: for thou art of those who are secure.
[028:032] "Move thy hand into thy bosom, and it will come forth white without stain (or harm), and draw thy hand close to thy side (to guard) against fear. Those are the two credentials from thy Lord to Pharaoh and his Chiefs: for truly they are a people rebellious and wicked."
[020:009] Has the story of Moses reached thee?
[020:010] Behold, he saw a fire: So he said to his family, "Tarry ye; I perceive a fire; perhaps I can bring you some burning brand therefrom, or find some guidance at the fire."
[020:011] But when he came to the fire, a voice was heard: "O Moses!
[020:012] "Verily I am thy Lord! therefore (in My presence) put off thy shoes: thou art in the sacred valley Tuwa.
[020:013] "I have chosen thee: listen, then, to the inspiration (sent to thee).
[020:014] "Verily, I am God: There is no god but I: So serve thou Me (only), and establish regular prayer for celebrating My praise.
[020:015] "Verily the Hour is coming - My design is to keep it hidden - for every soul to receive its reward by the measure of its Endeavour.
[020:016] "Therefore let not such as believe not therein but follow their own lusts, divert thee therefrom, lest thou perish!"..
[020:017] "And what is that in the right hand, O Moses?"
[020:018] He said, "It is my rod: on it I lean; with it I beat down fodder for my flocks; and in it I find other uses."
[020:019] (God) said, "Throw it, O Moses!"
[020:020] He threw it, and behold! It was a snake, active in motion.
[020:021] (God) said, "Seize it, and fear not: We shall return it at once to its former condition"..
[020:022] "Now draw thy hand close to thy side: It shall come forth white (and shining), without harm (or stain),- as another Sign,-
[020:023] "In order that We may show thee (two) of our Greater Signs.
[027:007] Behold! Moses said to his family: "I perceive a fire; soon will I bring you from there some information, or I will bring you a burning brand to light our fuel, that ye may warn yourselves.
[027:008] But when he came to the (fire), a voice was heard: "Blessed are those in the fire and those around: and glory to God, the Lord of the worlds.
[027:009] "O Moses! verily, I am God, the exalted in might, the wise!....
[027:010] "Now do thou throw thy rod!" But when he saw it moving (of its own accord)as if it had been a snake, he turned back in retreat, and retraced not his steps: "O Moses!" (it was said), "Fear not: truly, in My presence, those called as apostles have no fear,-
[027:011] "But if any have done wrong and have thereafter substituted good to take the place of evil, truly, I am Oft-Forgiving, Most Merciful.
[027:012] "Now put thy hand into thy bosom, and it will come forth white without stain (or harm): (these are) among the nine Signs (thou wilt take) to Pharaoh and his people: for they are a people rebellious in transgression."
There is also another account of night journey undertaken by Prophet Moses along with tribe of Israel is here :
[044:023] So go forth with My servants by night; surely you will be pursued:
[044:024] And leave the sea intervening; surely they are a host that shall be drowned.
The above mentioned night journeys of Prophet Moses has a neat link with verse 17:1 which mistakenly interpreted of Muhammad's . Moreover we have seen before , verse 17:2 mentioned Moses' name and verse 17:1 and 17:2 are separated by 'wa' (and) which suggest a continuation of the incident.