Some core-collapse supernovae are likely to be efficient cosmic-ray accelerators upto the PeV range, and therefore, to potentially play an important role in the overallGalactic 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.