Rodila se je [[Armenci v Iranu|armenski]] družini v [[Teheran|Teheranu]] v [[Iran|Iranu]].<ref>[http://www.farsnews.comir/newstext.php?nn=8607070625 Interview with Alenoush Terian, Farsnews Wire Service].</ref> Njen oče, ''Arto,'' je bil pesnik in prevajalec (s [[Psevdonim|psevdonimom]] ''Arizad''); prevedel jel [[Šahname|Shahnameh]] iz [[Perzijščina|perzijščine]] v [[Armenščina|armenščino]].<ref name="interview">{{Navedi splet|url=http://www.farheekhtegan.ir/content/view/8930/44/|archiveurl=https://archive.is/20120801154057/http://www.farheekhtegan.ir/content/view/8930/44/|archivedate=2012-08-01|title=An interview with Alenoush Terian|website=www.farheekhtegan.ir|language=fa}}</ref><ref>{{Navedi knjigo|title=Encyclopedia of Iranian Armenians|last=Janet D. Lazarian|year=2003|publisher=Hirmand Publisher|location=Tehran|isbn=964-6974-50-3|volume=|pages=426|editor-last=}}</ref>. Njena mama, ''Vartu,'' je bila odrska igralka in režiserka.<ref>{{Navedi knjigo|title=Encyclopedia of Iranian Armenians|last=Janet D. Lazarian|year=2003|publisher=Hirmand Publisher|location=Tehran|isbn=964-6974-50-3|volume=|pages=427|editor-last=}}</ref>
