MgB₂/MgO/MgB₂sandwich-type Josephson junctions have been fabricated using MgB₂films grown by hybrid physical-chemical vapor deposition (HPCVD). The MgO barrier and the insulating layer between wiring layers were made by RF magnetron sputtering. The junctions exhibit non-vanishingJ_cup to 40 K, theT_cof MgB₂. MgB₂wiring is achieved without significantly changing the junction properties. The fabrication and properties of the junctions are described in detail. TheI-Vcurves of the junctions are hysteretic at temperatures below 25 K and are RSJ-like above 25 K. Multiple Andreev reflection was observed, manifested by subgap peaks in the dI/dV-Vcurves and in good agreement with the theory. TheJ_cspread (1σ) of 10 junctions on one chip is better than 10%, which is likely due to the defects inside the MgO barrier as identified by transmission electron microscopy. Superconducting circuits made of these junctions may be expected to work at frequencies up to 1 THz or at temperatures over 20 K.