We propose a compact all-fiber Mach-Zehnder interferometer based on a dual core transversally chirped microstructured optical fiber to measure glucose concentration. The interrogation of the sensing device has been performed monitoring the wavelength shifts in the transmission spectrum in the infrared region. The response of the proposed device was evaluated when the glucose concentration changes from 70 g/L to 526 g/L at room temperature. The numerical results show that a high glucose concentration sensitivity of 3470 nm/RIU could be achieved with this configuration. Size, operational ranges and sensibilities of the proposed sensor allow it to be used in medical and biological applications.