This article presents a model-free deep reinforcement learning (DRL) approach for controlling a fiber drawing system. The custom DRL-based control system predictively regulates fiber diameter and produces a fiber with a desired, constant or nonconstant, diameter trajectory, i.e., diameter variation along the fiber length. Physical models of the system are not used. The system was trained and tested on a compact fiber drawing system, which has nonlinear delayed dynamics and stochastic behaviors. For a reference trajectory with random step changes, after 1 h of training, the DRL controller showed the same root-mean-squared error (RMSE) as an optimized PI controller; after 3 h of training, it achieved the performance of a quadratic dynamic matrix controller (QDMC). While the PI feedback controller showed 3.5 s of time lag in a step response, the DRL controller showed less than a second of time lag. Controller performance tests on trajectories not used in the training process are conducted; for a sine sweep reference trajectory, the DRL controller maintained an RMSE under 40 $\mu \text{m}$ up to a frequency of 45 mHz, compared to 25 mHz for QDMC.