In this work a novel design of a compact-size patch antenna is introduced for dual-band operation at 28/38 GHz. The antenna is constructed as a perforated resonant patch on a defected ground structure (DGS). The development stages of the design are described in detail. The patch is inset-fed through a microstrip line. A four-port MIMO antenna system is constructed using the proposed patch antenna. The antennas are arranged at the corners of a mobile handset in orthogonal orientations which results in polarizations and spatial diversities as well as low mutual coupling. The single antenna as well as the MIMO antenna system performance is assessed through numerical simulations and experimental measurements. The scattering parameters including the reflection and coupling coefficients are calculated using the commercially available CST® package and measured experimentally showing good agreement. The proposed antenna has a bandwidth of 0.6 GHz at 28 GHz and 1.17 GHz at 38 GHz. To evaluate the performance of the proposed MIMO antenna system, key performance parameters such as the radiation efficiency, envelope correlation coefficient (ECC), and diversity gain (DG) are investigated. The proposed four-port MIMO antenna system configuration is shown to be suitable for polarization and spatial diversity schemes as illustrated from the resulting radiation patterns. The proposed antenna has high radiation efficiency and the MIMO system has very good values for the ECC and DG over the operating frequency bands. The MIMO system possesses good polarization and spatial diversities with good isolation between the antennas without the use of any isolation enhancement techniques.