To answer this, it is important to understand that what we call a 'phalanx' was a group of guys with large shields and spears standing in close formation for protection. This was not unique to the Greeks, but was used throughout the ancient Near East. The Assyrians were one such example:
The sarissa phalanx was just an evolution of this, with the infantry still in close order, just using smaller shields and longer spears. So, if the phalanx was just guys with shields and spears in close formation, I think one can safely say it was used by many cultures after the Hellenistic period. The Strategikon of Maurice, which was composed in the 6th Century AD, listed the equipment of heavy infantry as including shields and lances. It also stated heavy infantry should be drawn up in the frontline, directly facing the enemy. Sounds pretty phalanxy, does it not?
The Germanic peoples also practice similar tactics. This consisted of what is popularly known as the shield-wall. Those who made use of a such formation include the Anglo-Saxons, Vikings, Franks, and other such cultures into the medieval period. One artistic source for this is the tapestry depicting the Battle of Hastings:
https://www.ancient.eu/uploads/images/9836.jpg?v=1608318903
I hope that answers your question sufficiently.
Sources
Maurice's Strategikon: Handbook of Byzantine Military Strategy, translated by George T Dennis
Warfare in the Barbarian West 450-900, by Guy Halsall
