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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 $Deltalesssim 1.4times 10^{-4}$ in order not to spoil the BBN epoch, which shows that the deformation from standard Bekenstein-Hawking expression should be small as expected.
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