Encrypted Traffic Classification (ETC) has become an important area of research with Machine Learning (ML) methods being the state-of-the-art. However, most existing solutions either rely on offline ETC based on collected network data or on online ETC with models running in the control plane of Software-Defined Networks (SDN), all of which do not run at line rate and would not meet latency requirements of time-sensitive applications in modern networks. This work leverages recent advances in data plane programmability to achieve real-time ETC in programmable switches at line rate, with high throughput and low latency. The proposed solution comprises (i) an ETC-aware Random Forest (RF) modelling process where only features based on packet size and packet arrival times are used, and (ii) an encoding of the trained RF model into production-grade P4-programmable switches. The performance of the proposed in-switch ETC framework is evaluated using 3 encrypted traffic datasets with experiments in a real-world testbed with Intel Tofino switches, in the presence of background traffic at 40 Gbps. Results show how the solution achieves high classification accuracy of up to 95%, with sub-microsecond delay, while consuming on average less than 10% of total available switch hardware resources.