The root derives from the noun سِجْن (sijn), which is borrowed from Byzantine Greek σίγνον (sígnon), from Latin sīgnum, so called because the Roman field standard (sīgnum), as well as the war chests and soldiers’ savings, were kept in the aedēs, in the center of the headquarters (principia). The eagle token being central to Roman ideology and religion, the warden of these monies was called sīgnifer and aquilifer and anything deposited there was brought ad signum. As this cellared building was well guarded, arrestees where brought thither – in Constantinople the praetōrium of the eparch of the city –, so the colloquial Greek attested from the 4th to 7th century used the phrase ἐν τοῖς σίγνοις (en toîs sígnois) for “into prison”.
Accordingly the Arabic سِجْن (sijn) is first attested by an (albeit like many possibly forged) verse of Umayya ibn Abī ṣ-Ṣalt أَيُّمَا شَاطِنٍ عَصَاهُ عَكَاهُ … ثُمَّ يُلْقَى فِي ٱلسِّجْنِ وَٱلْأَْكْبَالِ (ʔayyumā šāṭinin ʕaṣāhu ʕakāhu … ṯumma yulqā fī s-sijni wal-ʔakbāli), then in the Umayyad era by brigand-poets. That is because the nomadic Arabs, obviously, had no prisons, which were only known in the periphery settled by Byzantines, instead the outer punishment was exclusion from the tribal community which was likely to entail death. The other words دِيمَاس (dīmās) and مَطْمُورَة (maṭmūra) meaning places to lock up miscreants were Aramaic loanwords too.
As the occurrences of the word and derivatives in the Qurʾān are all from the Sūra Yūsuf and in 26:29 again about the Pharaoh threating with imprisonment, the term has been repeatedly suggested as mediated via Coptic, where the word also occurs, however it is just that the Pharaonic Egypt was imagined like the recent Greco-Roman Egypt, while Coptic was limited to Egypt, unlikely to lend any loanwords to Arabic before its Arab colonization, unlike Aramaic, where the Greek plural was borrowed, possibly heard by Arabs as its emphatic state to be clipped into the state سِجْن (sijn). But since Arabs were in Byzantine military service and its command language was Latin, till the 7th century ending bilingualism, it could well have been borrowed from either Greek or Latin directly.
س ج ن • (s-j-n)