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The $f(Q)$ theories of modified gravity arise from the consideration of non-metricity as the basic geometric quantity, and have been proven to be very efficient in describing the late-time Universe. We use the Big Bang Nucleosynthesis (BBN) formalism and observations in order to extract constraints on various classes of f(Q) models. In particular, we calculate the deviations that f(Q) terms bring on the freeze-out temperature in comparison to that of the standard $ΛCDM$ evolution, and then we impose the observational bound on $ |\frac{δ{T}_f}{{T}_f}|$ to extract constraints on the involved parameters of the considered models. Concerning the polynomial model, we show that the exponent parameter should be negative, while for the power-exponential model and the new hyperbolic tangent - power model we find that they pass the BBN constraints trivially. Finally, we examine two DGP-like $f(Q)$ models, and we extract the bounds on their model parameters. Since many gravitational modifications, although able to describe the late-time evolution of the Universe, produce too-much modification at early times and thus fall to pass the BBN confrontation, the fact that $f(Q)$ gravity can safely pass the BBN constraints is an important advantage of this modified gravity class.