Testing and calibration constitute a significant part of the overall manufacturing cost of microelectromechanical system (MEMS) devices. Developing a low-cost testing and calibration scheme applicable at the user side that ensures the continuous reliability and accuracy is a crucial need. The main purpose of testing is to eliminate defective devices and to verify the qualifications of a product is met. The calibration process for capacitive MEMS devices, for the most part, entails the determination of the mechanical sensitivity. In this work, a physical-stimulus-free built-in-self-test (BIST) integrated circuit (IC) design characterizing the sensitivity of capacitive MEMS accelerometers is presented. The BIST circuity can extract the amplitude and phase response of the acceleration sensor's mechanics under electrical excitation within 0.55% of error with respect to its mechanical sensitivity under the physical stimulus. Sensitivity characterization is performed using a low computation complexity multivariate linear regression model. The BIST circuitry maximizes the use of existing analog and mixed-signal readout signal chain and the host processor core, without the need for computationally expensive Fast Fourier Transform (FFT)-based approaches. The BIST IC is designed and fabricated using the 0.18-µm CMOS technology. The sensor analog front-end and BIST circuitry are integrated with a three-axis, low-g capacitive MEMS accelerometer in a single hermetically sealed package. The BIST circuitry occupies 0.3 mm2 with a total readout IC area of 1.0 mm2 and consumes 8.9 mW during self-test operation.