This list includes journals dedicated to the study of the Middle Ages as well as those that include medieval topics (denoted with an *)
The Burlington Magazine | The Burlington Magazine for Connoisseurs* (to 1947)
Journal of the Warburg and Courtauld Institutes*
Source: Notes in the History of Art
Studies in iconography | Studies in Iconography (online back issues)
Word and Image: A Journal of Visual/Verbal Inquiry*
Zeitschrift für Kunstgeschichte*
More medieval studies journals.