We find the Seiberg-Witten geometry for four dimensional N = 2 supersymmetric E₆ gauge theories with massless fundamental hypermultiplets, by geometrically embedding them in type II string theories compactified on Calabi-Yau threefolds. The resulting geometry completely agrees with that of recent works, which are based on the technique of N = 1 confining phase superpotentials. We also derive the Seiberg-Witten geometry for E₇ gauge theories with massive fundamental hypermultiplets.