The poet Rumi (1200s AD)
Arabic poetry has a long tradition in the Arabian peninsula even before the development of Islam. People composed and recited long poems that they remembered without writing down. As soon as written Arabic became common in the 700s AD, poets began publishing in every corner of the Islamic Empire.
One of the most famous of these poets is Omar Khayyam. Khayyam wrote in the 1100s AD. He may have been a follower of Sufi Islam, which is focused on the relationship between the individual and God. In any case, Khayyam's short poems remain difficult to interpret.
Here's a reading of one of Rumi's poems.
Rumi is another famous poet from the Islamic Empire. He wrote in the 1200s AD, a little before Dante in Europe. Rumi was certainly a follower of Sufi Islam. His poems are mainly about how love can connect people with God.
A third Sufi poet, Lalla Arifa, lived in northern India in the 1300s AD. She wrote poems about ordinary women's housework, used as metaphors, again, for people's relationship to God.