In insulators, the longitudinal resistivity becomes infinitely large at zero temperature. For classical insulators, the Hall conductivity becomes zero at the same time. However, there are special systems, such as two-dimensional quantum Hall insulators, in which a more complex scenario is observed at high magnetic fields. Here, we report experimental evidence for a quasiquantized Hall insulator in the quantum limit of the three-dimensional compound SrSi2. Our measurements reveal a magnetic-field range, in which the longitudinal resistivity diverges with decreasing temperature, while the Hall conductivity approaches a quasiquantized value that is given only by the conductance quantum and the Fermi wave vector in the field direction. The quasiquantized Hall insulator appears in a magnetic field induced insulating ground state of three-dimensional materials and is deeply rooted in quantum Hall physics.