The prophet Joel quotes Obadiah 17, which affirms that a remnant of Israel will escape the judgment of the eschatological day of the Lord. Joel quotes this as something “the Lord has said” (Joel 2:32) and as an explanation of his statement, “everyone who calls on the name of Yhwh shall be saved” (Joel 2:32).
Jeremiah also quotes from Obadiah extensively in Jeremiah 49 in an oracle against Edom (which is part of a larger section of oracles against the nations). Jeremiah does not include Obadiah’s warnings against Edom’s future actions against Jerusalem, likely because Edom violated those warnings in the 586 BC conquest of Jerusalem. In Jeremiah there are no further warnings, only the reiteration of judgment.
Jeremiah’s oracle against Edom is only one of a number found in the prophets, though the others are not directly dependent on Obadiah: “For other oracles about Edom, see Numbers 24:18; Isaiah 63:1–6; Jeremiah 9:24–25 (Eng., 9:25–26); 25:21; 27; 49:7–22; Ezekiel 25:12–14; 32:29; 35–36; Amos 1; 9:12; Joel 4:19 (Eng., 3:19); Malachi 1:2–5 (see also 2 Sam. 8:14; 2 Kgs. 8:20–22; 2 Chr. 21:8–10).”[1]
Finally, while one could argue that the Day of the Yhwh has clear background in the Pentateuch, the warnings of judgment in Deuteronomy 27-28, and (symbolically) in the Day of Atonement,[2] Obadiah is likely the first to use the “day” terminology that the rest of the prophets develop.
[1] Shepherd, KEL, 208.
[2] Matthew Aernie and Donald Hartley, The Righteous & Merciful Judge: The Day of the Lord in the Life and Theology of Paul, Studies in Scripture & Biblical Theology (Bellingham, WA: Lexham Press, 2018), 36. See especially the reference to “the day of their calamity” (Deut. 32:35). Block, ZECOT, 84.