Fluorescein Angiography (FA) is an imaging technique that allows to visualize the vascular structure of the retina. The Foveal Avascular Zone (FAZ) is a vessel-free area located at the center of the fovea whose shape characteristics are used to diagnose eye-related diseases such as diabetic retinopathy. Segmentation of the FAZ in FA therefore plays an important role in clinical decision making. However, manual delineation is costly and time-consuming. Current methods for automated FAZ segmentation either rely on segmenting the vasculature first, require manual initialization or are tailored to specific image properties. Hence, they often fail when dealing with images from clinical routine, which were usually acquired using multiple devices and at different imaging settings. In this paper we propose to overcome these limitations by means of a multitask learning approach. Our method exploits an additional Euclidean distance map prediction task to better deal with variable imaging conditions, by benefiting from its regularization effect. Our method is empirically evaluated using a data set of FA scans from large multicenter clinical trials with diverse qualities and image resolutions. The proposed model outperformed a baseline U-Net, achieving an average Dice of 0.805. To the best of our knowledge, our approach is the first deep learning method for FAZ segmentation in FA ever published.