Fisher information is a fundamental quantity in information theory and signal processing. A direct analytical computation of the Fisher information is often infeasible or intractable due to the lack or sophistication of statistical models. In this paper, we propose a Fisher Information Neural Estimator (FINE) which is computationally efficient, highly accurate, and applicable for both cases of deterministic and random parameters. The proposed method solely depends on measured data and does not require knowledge or an estimate of the probability density function and is therefore universally applicable. We validate our approach using some experiments and compare with existing works. Numerical results show the high efficacy and low-computational complexity of the proposed estimation approach.