The so called "Evil Eye" is a classic example of spiritual syncretism. It's origin is neither Christian nor Muslim — yet the belief system that it stands for has through long proximity been partially assimilated by adherents to both of of those religions.
It goes several names, but for example in Turkey it is usually known as Nazar. It is simply a symbol, usually a concentric pattern of circles in blue and white, that is supposed to ward off evil spirits. The symbol is so universal in Turkey that it is almost impossible to avoid. Even as a Christian with no interest in having them around I am constantly finding the things floating around my house. They are printed on receipts, dropped as tokens into shopping bags and boxes, woven into clothing, left behind by wary guests, and generally come out of the woodwork like dust bunnies.
The Nazar or Evil Eye symbol is actually just the most visible of many Animistic beliefs. The use of this symbol is actually fundamentally incompatible with Islam, but the two beliefs are widely practiced side by side and people are generally unaware of the conflict of interest they pose to each other.
In addition to being incompatible with Islam, belief in the Evil Eye to ward off evil spirits is almost universally seen as incompatible with the core doctrines of Christianity (as are almost all other incarnations of Animism). If some of our trust for safety is placed in something other than Christ, that thing becomes an idol that detracts from our focus on our Savior. The one who is able to protect us from all evil Spirits is the one who Himself triumphed over them:
Colossians 2:15 (ESV) He disarmed the rulers and authorities and put them to open shame, by triumphing over them in him.