  We analyze junction conditions at a null or non-null hypersurface $\Sigma$ in
a large class of scalar-tensor theories in arbitrary $n(\ge 3)$ dimensions.
After showing that the metric and a scalar field must be continuous at $\Sigma$
as the first junction conditions, we derive the second junctions conditions
from the Einstein equations and the equation of motion for the scalar field.
Subsequently, we study $C^1$ regular matching conditions as well as vacuum
conditions at $\Sigma$ both in the Jordan and Einstein frames. Our result
suggests that the following configurations may be possible; (i) a vacuum
thin-shell at null $\Sigma$ in the Einstein frame, (ii) a vacuum thin-shell at
null and non-null $\Sigma$ in the Jordan frame, and (iii) a non-vacuum $C^1$
regular matching at null $\Sigma$ in the Jordan frame. Lastly, we clarify the
relations between the conditions for $C^1$ regularity and also for vacuum
$\Sigma$ in the Jordan and Einstein frames.
