The distributed measurement of low pressure utilizing common optical fibers without sensitization is desired but challenging in many industrial applications. In this paper, with the assistance of machine learning, the distributed measurement of low hydrostatic pressure is realized based on optical carrier-based microwave interferometry (OCMI) employing the common single-mode fiber (SMF). Firstly, the theoretical model of pressure sensitivity is established, and further investigated and validated by numerical simulation and finite element simulation. Subsequently, a distributed hydrostatic pressure measurement experiment is conducted utilizing a common SMF with cascaded weak light reflectors processed along the fiber core. The results indicate that it is difficult to measure low pressure through common fibers based on the traditional demodulation method. To overcome the above limitations, we propose to employ machine learning to analyze the microwave interference information, in order to achieve a one-to-one mapping with the hydrostatic pressure exerted on the sensing fiber. The implementation of distributed pressure measurement is based on the unique advantages of OCMI in terms of physical positioning and reconfigurable gauge length. Meanwhile, different microwave interferometric information is employed as inputs for comparison to select the most effective signals for optimal prediction. The results show that a satisfactory overall measurement and distributed measurement of low hydrostatic pressure can be achieved with the assistance of machine learning, where the accuracy of distributed measurement increases with the increase of Fabry-Perot interferometer (FPI) cavity length. The proposed strategy can be extended to other relatively short-distance spatially continuous distributed or long-distance quasi-distributed fiber sensing systems.