  Some core-collapse supernovae are likely to be efficient cosmic-ray
accelerators up to the PeV range, and therefore, to potentially play an
important role in the overall Galactic cosmic-ray population. The TeV gamma-ray
domain can be used to study particle acceleration in the multi-TeV and PeV
range. This motivates the study of the detectability of such supernovae by
current and future gamma-ray facilities. The gamma-ray emission of
core-collapse supernovae strongly depends on the level of the two-photon
annihilation process: high-energy gamma-ray photons emitted at the expanding
shock wave following the supernova explosion can interact with soft photons
from the supernova photosphere through the pair production channel, thereby
strongly suppressing the flux of gamma rays leaving the system. In the case of
SN 1993J, whose photospheric and shock-related parameters are well measured, we
calculate the temporal evolution of the expected gamma-ray attenuation by
accounting for the temporal and geometrical effects. We find the attenuation to
be of about $10$ orders of magnitude in the first few days after the SN
explosion. The probability of detection of a supernova similar to SN 1993J with
the Cherenkov Telescope Array is highest if observations are performed either
earlier than 1 day, or later than 10 days after the explosion, when the
gamma-ray attenuation decreases to about $2$ orders of magnitude.
