We introduce a superpotential for partial flag varieties of type $A$. This is a map $W: Y^circ to mathbb{C}$, where $Y^circ$ is the complement of an anticanonical divisor on a product of Grassmannians. The map $W$ is expressed in terms of Plucker coordinates of the Grassmannian factors. This construction generalizes the Marsh--Rietsch Plucker coordinate mirror for Grassmannians. We show that in a distinguished cluster chart for $Y$, our superpotential agrees with earlier mirrors constructed by Eguchi--Hori--Xiong and Batyrev--Ciocan-Fontanine--Kim--van Straten. Our main tool is quantum Schubert calculus on the flag variety.
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