Are Edomites the same as modern Arabs?

No. Edomites descend from Esau, Jacob's twin brother through Isaac and Abraham; Arabs primarily descend from Ishmael, Abraham's other son. Edom was absorbed into Judea by 125 BC and dissolved as a distinct people after AD 70.

No — and the Bible is unusually specific about this.

Edom is Esau, Jacob's twin brother. Genesis traces the line directly: Isaac fathered Jacob and Esau (Genesis 25:24–26), and Esau became the father of Edom (Genesis 36:1). That makes Edomites descendants of Abraham through Isaac — the same line as Israel, just through the other twin. The Torah draws out the implication explicitly:

"You shall not abhor an Edomite, for he is your brother." — Deuteronomy 23:7

Arabs, by contrast, are primarily traced to Ishmael (יִשְׁמָעֵאל), Abraham's first son through Hagar. Genesis 25:12–18 names twelve Ishmaelite tribes and places them from Havilah to Shur — the Arabian peninsula. Ishmael and Esau are not the same line. They are two different sons of Abraham who fathered two different peoples.

What actually happened to the Edomites is its own story. Between the 4th and 3rd centuries BC, Nabataean Arabs pushed the Edomites out of their ancestral territory in Seir and into the Negev, where they became known as Idumeans. In 125 BC, the Jewish ruler John Hyrcanus conquered Idumea and forcibly converted the population to Judaism (the historian Josephus records this in Antiquities 13.9.1). Herod the Great — the king who ruled when Jesus was born — was an Idumean. After the Roman destruction of Jerusalem in AD 70, the Idumeans disappeared from history as a distinct ethnic group, absorbed into the surrounding populations.

So when Obadiah prophesies against Edom, he is not prophesying against any modern nation. The Edomites as a people stopped existing almost two thousand years ago.

That said, the book itself broadens its scope in verse 15:

"For the day of Yahweh is near upon all the nations. As you have done, it will be done to you." — Obadiah 1:15

Edom is named specifically as a historical target (their betrayal of Jerusalem in 586 BC is what the book addresses), but the text itself tells us Edom also becomes paradigmatic — the specific case that reveals the universal principle. What Edom did, any nation can do; what happens to Edom, Yahweh says, will happen to every nation that does the same.

The rabbis after AD 70 often used "Edom" as a code name for Rome. The point was not genetic descent — it was pattern. The brother who stands at the crossroads watching the defenseless flee is judged by the same measure, regardless of when or where.

For the full treatment of Edom's history, the shared oracle with Jeremiah 49, and what "brother" means in the charge, read the study on Obadiah.