Mujeeb's exploration of the Islamic(ate) world traverses multiple disciplines and aspects of Islam, the Arab-Islamic world, and the cross-cultural traditions from medieval Western Eurasia through to the modern world, including the medieval and early modern Greater Asia (Central Asia, South Asia, and East Asia in addition to West Asia and North/West Africa). Currently, his has interests in the medical literary traditions of the Islamicate world, which is a term to describe the cultures and civilizations that flourished under the cultural spheres ruled by Muslims. For example, medicine was introduced as a complete tradition through translation both directly from Greek as well as through Syriac intermediaries into Arabic not to mention translations from Pahlavi, Sanskrit, and other sources. Mujeeb explores the period that follows this introduction to explore the development of the medical tradition, especially medical writing.
Mujeeb is also interested in Islam in non-Muslim-majority contexts and less explored areas such as early modern China and modern Japan, two areas of research which have seen an increase in the quality and amount of scholarly literature in the past decade.
Mujeeb's interest in the Arab-Islamic world revolves around how Muslims understood the foreign, both in the medieval period following the translation movement and subsequent to the introduction of early modern European thought. He is also deeply interested in the Islamic legal traditions, especially the four Sunni schools of law.