This paper investigates the impact of the recently proposed concept of fluid reconfigurable intelligent surfaces (FRIS) on covert communications. Specifically, we consider a communication scenario where a legitimate transmitter aims to covertly deliver information to its intended receiver through a planar FRIS, while an adversary attempts to detect whether any transmission is occurring. In this context, we analyze the false alarm (FA) and missed detection (MD) probabilities, and derive a closed-form expression for the covertness outage probability (COP). Furthermore, the success probability is characterized under the optimal detection threshold, providing new insights into the trade-off between covertness and reliable transmission. Numerical results reveal that FRIS provides a clear advantage over fixed-position RIS at low-to-moderate transmit powers by improving reliability and enhancing covertness, while at very high power levels, fixed-position RIS may sustain slightly higher success probability due to reduced leakage toward the adversary.