In this paper, the enhancement of gain and bandwidth of a Minkowski fractal antenna (MFA) with defected ground structure is investigated. The antenna characteristics are studied for first and second iterations by considering complementary split ring resonators in the L-shaped modified ground plane. The dimensions of the MFA are optimized with computer simulation technology software and the fabricated antenna characteristics are measured using Vector Network Analyzer and Wave and Antenna Training System. From the simulation, the maximum gain of our proposed antenna has been found 5.2 dB. Both bandwidths obtained from simulation and measurement exceed 2 GHz. The results of simulation are in good agreement with measured ones. This proposed antenna is suitable for the applications of various 5G wireless communications.