Event cameras capture visual information with a high temporal resolution and a wide dynamic range. This enables capturing visual information at fine time granularities (e.g., microseconds) in rapidly changing environments. This makes event cameras highly useful for high-speed robotics tasks involving rapid motion, such as high-speed perception, object tracking, and control. However, convolutional neural network inference on event camera streams cannot currently perform real-time inference at the high speeds at which event cameras operate - current CNN inference times are typically closer in order of magnitude to the frame rates of regular frame-based cameras. Real-time inference at event camera rates is necessary to fully leverage the high frequency and high temporal resolution that event cameras offer. This paper presents EvConv, a new approach to enable fast inference on CNNs for inputs from event cameras. We observe that consecutive inputs to the CNN from an event camera have only small differences between them. Thus, we propose to perform inference on the difference between consecutive input tensors, or the increment. This enables a significant reduction in the number of floating-point operations required (and thus the inference latency) because increments are very sparse. We design EvConv to leverage the irregular sparsity in increments from event cameras and to retain the sparsity of these increments across all layers of the network. We demonstrate a reduction in the number of floating operations required in the forward pass by up to 98%. We also demonstrate a speedup of up to 1.6X for inference using CNNs for tasks such as depth estimation, object recognition, and optical flow estimation, with almost no loss in accuracy.