Cleopatra was Macedonian Greek, of the Ptolemy dynasty. The Ptolemaic Kingdom was created by Ptolemy, one of the Generals of Alexander the Great.
It was a Macedonian royal family and regime which ruled over Egypt at the time, even though all local Egyptian practises were kept intact. They ruled as traditional Pharaohs.
After the death of Alexander the Great, his Generals carved up the Empire between each other, this included the Ptolemaic Kingdom of Egypt, the Seleucid Empire which ruled from the Syria to modern Pakistan, and even a Greek Buddhist state, the Greco-Bactrian Kingdom, ruling on the borders of India for hundreds of years.
Cleopatra VII: