Laser diodes operating in the 2.3-μm band are attractive for detecting trace carbon oxide (CO) gas because of the strong absorption lines of CO and weak interference from H2O in this band. As a light source for CO-gas detection, we previously developed a 2.3-μm-band distributed feedback (DFB) laser with InAs/InGaAs multiple quantum wells (MQWs) grown on InP. To construct a high-speed with high-accuracy measurement system for CO, the light source must be capable of fast wavelength tuning over a wide range. In this study, we developed InAs/InGaAs distributed Bragg reflector (DBR) laser operating in the 2.3-μm band that uses current injection and has wider and faster wavelength tuning compared with DFB lasers using chip-temperature control. The laser cavity consists of an active region with InAs/InGaAs MQWs, front/rear DBR regions, and phase-control region. The DBR and phase-control regions are monolithically integrated with the active region by using the butt-joint technique. The measured lasing wavelength was 2348.1 nm with an injection current for the active region of 100 mA at room temperature and under continuous wave operation. When the DBR current (front + rear) increased from 0 to 100 mA, the lasing wavelength shifted by -12.0 nm. The estimated refractive index change was 0.51%, which is comparable to that of conventional devices operating in the telecommunication band. Furthermore, by sweeping the currents for the DBRs and phase-control region, the lasing wavelength could be continuously tuned over a range of 4.2 nm, which covers multiple CO absorption lines in the 2.3-μm band.