Islam is as opposed to Arianism as it is to orthodox Christian teaching on the person of Christ and his relationship with God. That is why Islam makes no distinction between modern-day Arians (such as the Jehovah’s Witnesses) and the bulk of Christian denominations that eschew Arianism. They all believe in God as “Father” and as Christ as “the Son of God” which, to Muslims, is the sin of “shirk” – ascribing ‘partners’ to God. However, once we grasp what Arius actually taught on this subject, we are in a better position to have meaningful dialogue with those who reject the Christian Trinity doctrine.
Arius was the presbyter whose doctrine of the co-eternity of the Logos (the Word who became the man, Jesus) caused the Council of Nicaea in 325 A.D. A reading of John’s gospel, the first chapter, is vital to know the significance of the one named as ‘the Word’ who ‘became flesh’ - the man, Jesus Christ. Arius believed there was a time when the Logos did not exist. When the Bible spoke of the Father 'begetting' the Son, Arius said that was a synonym for 'creating'; the perfect creature through whom all other things were made.
Arius's theology was that Christ did not possess deity by nature but developed into it by virtue of his constant and growing moral unity with God - he furnished the perfect example of commitment to the good and to God. Such a view hardly differs from the teaching of Adoptionism.
Arius's view of Christ is that God created him to be mediator, as in the Neoplatonic concept of the Logos. His ideas helped the 'conversion' of countless pagans during Constantine's era as they sharply reduced the clash between Christianity and pagan philosophical monotheism. Interestingly, Arius was ready to pray to Jesus and give him relative worship. When a creature is worshipped as ‘a god’, not the same God as the Father, then Christian monotheism has been violated. That is why Christianity has always maintained that Christ was never created – never had a starting point in time – that the one Being of God subsists in the three uncreated, co-equal ‘persons’ of the Father, the Son, and the Holy Spirit. All Catholics, Orthodox and Protestants agree on this, but Arians (and their modern-day counterparts) disagree.
That is why the step of saying this creature was the supreme archangel, Michael, naturally follows from the initial claim that the Son was created. The logic is that if the Father only created one creature, who was to be supreme in heaven, that would have to be the first angel who was superior to all other angels. However, the theological work of Tertullian (A.D. 160 - 230) gave the basis for refuting Arius, and his theology was accepted a century before Arius came along with his! Modern-day Arians, such as the Jehovah's Witnesses (who say Jesus is the Archangel, Michael) never admit that Trinitarian beliefs were expressed as sound theology a century before Arius.
I have gleaned that from the massive book, Heresies and Orthodoxy in the History of the Church by Harold O.J. Brown, pp 108-117 (Hendrickson/Baker 1998). It gives an excellent explanation on such historical matters as they relate to Christian theology.
This serves to show that Islam is not influenced by Arianism, rejecting it just as much as they do orthodoxly Christian teaching that also rejects Arianism.