  We use Big Bang Nucleosynthesis (BBN) data in order to impose constraints on
the exponent of Barrow entropy. The latter is an extended entropy relation
arising from the incorporation of quantum-gravitational effects on the
black-hole structure, parameterized effectively by the new parameter $\Delta$.
When considered in a cosmological framework and under the light of the
gravity-thermodynamics conjecture, Barrow entropy leads to modified
cosmological scenarios whose Friedmann equations contain extra terms. We
perform a detailed analysis of the BBN era and we calculate the deviation of
the freeze-out temperature comparing to the result of standard cosmology. We
use the observationally determined bound on $ |\frac{\delta {T}_f}{{T}_f}|$ in
order to extract the upper bound on $\Delta$. As we find, the Barrow exponent
should be inside the bound $\Delta\lesssim 1.4\times 10^{-4}$ in order not to
spoil the BBN epoch, which shows that the deformation from standard
Bekenstein-Hawking expression should be small as expected.
