We have fabricated planar thin-film MgB2 Josephson junctions and 20-junction series arrays using 200-keV ion implantation and electron-beam lithography. Resistively shunted junction I-V characteristics were observed in the temperature range of 34–38K. The ac Josephson effect was observed and flat giant Shapiro steps in arrays suggest good junction uniformity with a small spread in junction parameters. The temperature dependence of the critical current suggests that the nature of the interface between the superconductor and normal region can be described using a soft boundary proximity effect coupling model. We believe that the higher operating temperature and close spacing of these junctions make them promising candidates for quantum voltage standards and other devices.