JWST is providing a unique opportunity to directly study the feedback processes regulating star formation (SF) in early galaxies. The two z > 5 quiescent systems (JADES-GS-z7-01-QU and MACS0417-z5BBG) detected so far show a recent starburst after which SF is suppressed. To clarify whether such quenching is due to supernova (SN) feedback, we have developed a minimal physical model. We derive a condition on the minimum star formation rate,
SFR
min
, lasting for a time interval Δt
b
, required to quench SF in a galaxy at redshift z, with gas metallicity Z, and hosted by a halo of mass M
h
. We find that lower (z, Z, M
h
) systems are more easily quenched. We then apply the condition to JADES-GS-z7-01-QU (z = 7.3, M
⋆ = 108.6
M
⊙) and MACS0417-z5BBG (z = 5.2, M
⋆ = 107.6
M
⊙) and find that SN feedback largely fails to reproduce the observed quenched SF history. Alternatively, we suggest that SF is rapidly suppressed by radiation-driven dusty outflows sustained by the high specific star formation rates (43 and 25 Gyr−1, respectively) of the two galaxies. Our model provides a simple tool to interpret the SF histories of post-starburst galaxies and unravel quenching mechanisms from incoming JWST data.