Hydrogen-fueled engines require large values of the excess air ratio in order to achieve high thermal efficiency. A low value of this coefficient promotes knocking combustion. This paper analyzes the conditions for the occurrence of knocking combustion in an engine with a turbulent jet ignition (TJI) system with a passive pre-chamber. A single-cylinder engine equipped with a TJI system was running with an air-to-fuel equivalence ratio λ in the range of 1.25–2.00, and the center of combustion (CoC) was regulated in the range of 2–14 deg aTDC (top dead center). Such process conditions made it possible to fully analyze the ascension of knock combustion until its disappearance with the increase in lambda and CoC. Measures of knock in the form of maximum amplitude pressure oscillation (MAPO) and integral modulus of pressure oscillation (IMPO) were used. The absolute values of these indices were pointed out, which can provide the basis for the definition of knock combustion. Based on our own work, the MAPO index > 1 bar was defined, determining the occurrence of knocking (without indicating its quality). In addition, taking into account MAPO, it was concluded that IMPO > 0.13 bar·deg is the quantity responsible for knocking combustion.