In this paper, we propose a privacy-preserving event-triggered quantized average consensus algorithm that allows agents to calculate the average of their initial values without revealing to other agents their specific value. We assume that agents (nodes) interact with other agents via directed communication links (edges), forming a directed communication topology (digraph). The proposed distributed algorithm can be followed by any agent wishing to maintain its privacy (i.e., not reveal the initial value it contributes to the average) to other, possibly multiple, curious but not malicious agents. Curious agents try to identify the initial values of other agents, but do not interfere in the computation in any other way. We develop a distributed strategy that allows agents while processing and transmitting quantized information, to preserve the privacy of their initial quantized values and at the same time to obtain, after a finite number of steps, the exact average of the initial values of the nodes. Illustrative examples demonstrate the validity and performance of our proposed algorithm.