The use of a two-stage combustion system in a hydrogen-fueled engine is characteristic of modern internal combustion engines. The main problem with hydrogen combustion in such systems is knocking combustion. This paper contains the results of research under knock combustion conditions with a single-cylinder internal combustion engine equipped with a turbulent jet ignition system (TJI). A layout with a passive pre-chamber and a variable value of the excess air ratio range λ = 1.25–2.0 with a constant value of the center of combustion (CoC = 4 deg) after top dead center (TDC) was used. Two indicators of knock combustion were analyzed: maximum oscillation of pressure and the Mahle Knock Index. Analyses were also carried out taking into account the rate of heat release and the amount of heat released. As a result of the investigation, it was found that knock combustion occurs intensively at small values of the air excess ratio. Hydrogen knock combustion disappears for λ = 2.0 and greater. The pressure oscillation index was found to be more applicable, as its limiting value (>1 bar) allows easy diagnosis of knock combustion. The Mahle Knock Index is a quantity that allows interval analysis of the knock. The choice of classes and weighting coefficients requires an iterative operation, as they strictly depend on engine characteristics, load, and knock magnitude.