Markov Chain Monte Carlo (MCMC) methods are widely used for Bayesian inference in astronomy. However, when applied to datasets coming from next-generation telescopes, inference becomes computationally expensive. We propose using amortized variational inference to estimate the posterior of a supernova light curve parametric model. We show that amortization with a recurrent neural network is significantly faster than MCMC while providing competitive estimates of the predictive distribution. To the best of our knowledge, this is the first time this fast amortized framework is applied to astronomical light curves. This approach will be essential when estimating the posterior of astrophysical parameters for terabytes of data per night that next-generation telescopes will produce.