The short answer is... why would he? At the time Herodotus was writing, the Jews were a tiny inland people-group within the world-spanning Persian empire. The Achaemenids ruled over hundreds of minor tribes within their borders in addition to the great peoples of Persia, Egypt, Babylon, Elam, etc.

The power or population of Hebews/Jews/Israelites/Judahites was never especially noteworthy even in their cramped and crowded corner of the world. At their height, they had dominance over a few similarly tiny peoples within a tiny area. For most of their history, they were just one of many groups struggling to survive. And by the lifetime of Herodotus, they were diminished even beyond that. The conquest of Judah and the exile of its elite had dispersed many of them around the known world. When the Persians sponsored a return of the exiles to Jerusalem and the reconstruction of its Temple and walls, it took decades for the work to be completed.

Herodotus does mention the coastal area of the region, "Palestine," in a few places, always as a "district of Syria," and refers to the Phoenicians who dwell there. He does refer to the custom of circumcision as practiced by the Egyptians, Ethiopians, and Syrians (among whom he numbered the people of Palestine). The Phoenicians of Palestine were numerous, wealthy, and warlike enough (according to Herodotus's inflated figures) to muster 300 ships and warriors to crew them to serve in the Persian army. But he is not interested in the Jews any more than he is in any of the other minor tribes of the hinterlands.

(Minor note: at a stretch, one can imagine that the second passage linked above at least partially refers to the Jews in Herodotus's typically garbled way... in particular through the reference to migration from the Red Sea. But the people he refers to are a seafaring people, quite unlike the highland Hebrews. It is possible that some Hebrews were among their number, but the contingent described sounds very much like what one might expect of the seafaring peoples of the Levantine coast).

The fascinating thing about the Jewish (or Hebrew/Israelite/Judahite) place in history is that they weren't really ever a major power in a political or military sense. Their impact came in the areas of culture and religion, despite material poverty, political powerlessness, and economic insignificance. And the biblical authors were well aware of this fact: Deut 7:7 says (in the voice of YHWH) "It was not because you were larger than all other people that YHWH loved you and chose you. Indeed, you were the smallest of peoples!"