Solar radio spikes are short lived, narrow bandwidth features in low frequency solar radio observations. The timing of their occurrence and the number of spikes in a given observation is often unpredictable. The high temporal and frequency of resolution of modern radio telescopes such as NenuFAR mean that manually identifying radio spikes is an arduous task. Machine learning approaches to data exploration in solar radio data is on the rise. Here we describe a convolutional neural network to identify the per pixel location of radio spikes as well as determine some simple characteristics of duration, spectral width and drift rate. The model, which we call SpikeNet, was trained using an Nvidia Tesla T4 16GB GPU with ~100000 sample spikes in a total time of 2.2 hours. The segmentation performs well with an intersection over union in the test set of ~0.85. The root mean squared error for predicted spike properties is of the order of 23%. Applying the algorithm to unlabelled data successfully generates segmentation masks although the accuracy of the predicted properties is less reliable, particularly when more than one spike is present in the same 64 X 64 pixel time-frequency range. We have successfully demonstrated that our convolutional neural network can locate and characterise solar radio spikes in a number of seconds compared to the weeks it would take for manual identification.