Phonon lasers have long been a subject of interest and possess broad application prospects. Much effort is devoted to lay the foundation of realizing phonon lasers using cavity magnomechanical systems, but up to now no related work is carried out to explore the quantum‐squeezing‐engineered phonon laser action in cavity magnomechanics. Here, the phonon laser action is investigated in a three‐mode cavity magnomechanical system built based on a microwave resonator‐yttrium iron garnet sphere composite device, focusing on the effect induced by the magnon‐mode squeezing. It is found that the magnon squeezing can improve the effective magnon–photon and magnon–phonon coupling rates. It is demonstrated that the phonon laser action can be engineered and enhanced by changing the squeezing strength. This scheme provides a new mechanism to improve the effective magnon–photon and magnon–phonon couplings for various applications, and demonstrates the feasibility of realizing high‐gain and low‐threshold phonon lasers with cavity magnomechanical platforms.