The building that houses the museum was constructed on the order of Sultan Bayezid II, son of Mehmed the Conqueror, as part of the Bayezid II Mosque complex. The mosque itself was completed in 1505 — one of the great early Ottoman mosques of Istanbul, its design a direct precursor to the later imperial style. The madrasa followed immediately afterward, its construction begun after the mosque's completion and finished by 1507. A madrasa was a school of religious and legal learning, attached to mosques throughout the Islamic world; the students who studied here would have learned Quranic sciences, law, and the arts of the book. That the building now displays the calligraphic art those students would have practiced and revered is a pleasing continuity, five centuries collapsed into a single courtyard.

Islamic calligraphy developed over more than a millennium into one of the world's most refined visual traditions. The Arabic script — used not just for Arabic but for Persian, Ottoman Turkish, and other languages across a vast geographic range — offered calligraphers an extraordinary range of forms to work with: scripts that could be compressed or elongated, angular or flowing, monumental or intimate. The major styles — Naskh, Thuluth, Diwani, Nastaliq, among others — each have their own conventions and aesthetic registers, their own appropriate contexts and characteristic moods. The museum's collection of 3,121 pieces spans this range. Some works are large, designed to hang above a mosque's entrance or doorway; others are intimate, made for private devotion or contemplation. What unites them is the conviction that the word, properly written, is a form of beauty.

The institution has not always had its current home or its current name. It was first opened in 1968 as the 'Writing Museum,' established in the madrasa of the Yavuz Selim Complex — another Ottoman imperial site, on the ridge above the Golden Horn. For sixteen years it operated there, before being moved in 1984 to its present location in the Bayezid madrasa and renamed the Museum of Turkish Calligraphy Art. The move brought it to Beyazıt Square, one of Istanbul's most historically charged public spaces — the site of the Byzantine Forum of Theodosius, now anchored by the great mosque and the gatehouse of Istanbul University. For a museum dedicated to the art of Ottoman letters, the setting could hardly be more fitting.

In 2015, the museum closed for restoration. As of 2020, it had not yet reopened — a reflection of both the scale of the work required and the slower rhythms with which historic buildings are sometimes cared for. The closure means visitors arriving at Beyazıt Square in search of the collection may find the madrasa shuttered, its courtyard quiet. But the building itself remains visible, its Ottoman stonework and domed cells facing the square as they have for more than five hundred years. Restoration, when it is complete, will return the collection to public view — 3,121 works of calligraphic art waiting in the kind of patient silence that suits them. The Beyazıt Mosque still calls the faithful to prayer next door, as it has since 1505. Some continuities in Istanbul feel entirely natural.