I did not find a clear definition of grace (of Christianity). But, I can try relating different aspects of the definition I found in wiki to that of Islam from mostly from Qur'an.
Grace in Christianity is the free and unmerited favour of God as manifested in the salvation of sinners and the bestowing of blessings
So which of the favors of your Lord would you deny? [Qur'an 55:13]
The whole Chapter Ar-Rahman sets the context of that one line which is highly repeated.
Common Christian teaching is that grace is unmerited mercy (favor) that God gave to humanity by sending his son to die on a cross, thus delivering eternal salvation.
Indeed, in this [Qur'an] is notification for a worshipping people. And We have not sent you, [O Muhammad], except as a mercy to the worlds. [Qur'an 21:106-107]
implying God sent Muhammad as a prophet (not as son) to remind everyone, even those who don't deserve. But, the reminder / blessings will be taken only by those who fear. But, definitely no concept of son's sacrifice in Islam.
And the child (Jesus) grew, and waxed strong in spirit, filled with wisdom: and the grace of God was upon him. [Luke 2:40]
the same thing in Qur'an
And when Jesus brought clear proofs, he said, "I have come to you with wisdom and to make clear to you some of that over which you differ, so fear Allah and obey me. [Qur'an 43:63]
And We gave to Abraham, Isaac and Jacob - all [of them] We guided. And Noah, We guided before; and among his descendants, David and Solomon and Job and Joseph and Moses and Aaron. Thus do We reward the doers of good. [Qur'an 6:84]
In this example (of Luke 2:40 above) when using the definition of grace to mean unmerited favor it does not make sense, to some, that the sinless Christ would need this..... This at its root means literally Christ dispenses Gods grace from himself.
There is nothing like that in Islam.
Equally some say, how can one fall short of grace? (Galatians 5:4) or meekness attract it and pride repel it (James 4:6) if it is unmerited.
The answer to this is,
...For indeed, Allah sends astray whom He wills and guides whom He wills....[Qur'an 35:8]
And the solution is given as, one should remember God as much as he can.
Alternatively Bill Gothard has suggested "God's grace gives us the desire and the power to do his will.
If I understood it right, irrespective of what you believe God's grace is, I can best relate it to the term 'guidance' which is frequently used in the Qur'an.