Along with the rapid growth and rise to prominence of food delivery platforms, concerns have also risen about the terms of employment of the ``gig workers'' underpinning this growth. Our analysis on data derived from a real-world food delivery platform across three large cities from India show that there is significant inequality in the money delivery agents earn. In this paper, we formulate the problem of fair income distribution among agents while also ensuring timely food delivery. We establish that the problem is not only NP-hard but also inapproximable in polynomial time. We overcome this computational bottleneck through a novel matching algorithm called FairFoody. Extensive experiments over real-world food delivery datasets show FairFoody imparts up to 10 times improvement in equitable income distribution when compared to baseline strategies, while also ensuring minimal impact on customer experience.