To clarify, are you asking about modern historians writing the histories of their own nations in the same way that European and American academics tend to do, or about works from historical persons who lived in the period in which they were writing about (analogous to a Herodotus or Tabari-type)?

The quintessential example would be Ibn Khaldun, whose Muqaddimah is considered by many historians of history to be one of the first attempts at an objective history. Ibn Khaldun was from contemporary Morocco, but moved around a lot. The book is massive and monumental, but finding a translation of the entire text is somewhat difficult (I'm not actually certain the entirety has been translated, in fact).

Just to give a taste: Egyptian historians include al-Maqrizi from the 14th century (Al-Mawāʻiẓ wa-al-Iʻtibār bi-Dhikr al-Khiṭaṭ wa-al-āthār, commonly known as the Khiṭaṭ), al-Jabarti (18th/19th century; ‘Aja’ib al-athar fi’l-tarajim wa’l-akhbar), Amin Sami (Taqwim al-Nil), and contemporary historians like Abd al-Rahman al-Rafi'i -- the issue is that a lot of these haven't been fully translated from the original Arabic into other languages, but they were influential writers.

Contemporary Moroccan and Algerian historians often write in French -- and, again, a lot of these haven't been translated into English (or, often, Arabic), which tends to be an issue with scholarship on the former French colonies as a whole.