Egypt under Roman rule does not fall into antiquity (the "ancient era") but into the classical era. Ancient Egypt fell to the Persians in 343 BC. One of Alexander the Great's generals became the ruler of Egypt right after that, and that was the end of Ancient Egypt. The last ruler of this Ptolemaic line was Cleopatra, and after her, Egypt was annexed into Rome.
The Egypt you have in mind, with the worship of ancient Egyptian deities, is already gone under the Roman Empire, as Egyptians all became Christians, long before the Muslim invasion (Think who the Christians in Alexandria were when the Great Library was destroyed in 391 AD).
Roman Egypt was part of the Byzantine Empire, so it did not fall with the fall of the West Roman Empire. But the Islam Empire conquered Egypt in the 7th century, so that marks the conversion of Egypt to the region that you know of today.
You're probably also wondering when the Egyptians stopped speaking Egyptian and started speaking Arabic. The beginning of that would also be the 7th century. Ancient Egyptian survives today in the form of the Coptic language, and unsurprisingly, it is still used as the liturgical language of the Coptic Church.
You're probably also wonder when did Egyptian hieroglyphs die out. The Rosetta Stone is from the times of Ptolemaic Egypt. The ruler's langauge was Greek, and they had a translation of that in hieroglyphs. This also died out under Roman rule. The last known inscription with hieroglyphs is from 394 AD.
So long before Egypt became Muslim, it was already assimilated by the Greeks and Romans.
https://www.quora.com/What-was-the-end-of-Ancient-Egypt
