Zymvrakakis was born to Cretan Charalambos Zymvrakakis in Nafplio, Argolis in 1861. He graduated the Greek Military Academy and was named 2nd Lieutenant in 1881, continuing his studies at Orléans in France.
In 1897, he volunteered for and fought in the Cretan Revolt. He later became an active member of the Military League, and it was he who suggested, following the Goudi movement, to call upon the Cretan Eleftherios Venizelos to come to Greece. Subsequently he served as adjutant to King George I, was appointed commanding officer of the newly raised 11th Infantry Division at Thessaloniki (late 1913) and was promoted to the rank of Major General on 8 December 1914.
A close friend and supporter of Venizelos, Zymvrakakis was instrumental in the revolt that led to the establishment of the pro-Venizelist and pro-Allied "State of National Defence" in northern Greece during World War I. He led the first Greek units on the Macedonian front, and commanded the Greek forces in the Battle of Skra ( May 29 - May 30, 1918). Subsequently he was tasked with the occupation of Western and Eastern Thrace, territories that had been ceded to Greece from Bulgaria and the Ottoman Empire respectively. In the latter case he defeated the resistance offered by the remaining Ottoman forces in the region.
Following the electoral defeat of the Venizelists in November 1920, he was dismissed from his post.
Zymvrakakis died in Athens in 1928.