Cryogenic electron tomography (cryo-ET) is a technique to produce highly detailed 3D images (called tomograms) of cellular environments. Cryo-ET is currently the only technique that can achieve near-atomic resolution of proteins and cellular structures in their native environment. An essential step of cryo-ET analysis techniques targeted at protein structure determination is to find all instances of the protein of interest in the tomograms, a task known as particle picking. Due to the low signal-to-noise ratio, presence of artifacts and vast diversity in target proteins, particle picking is a challenging 3D object detection problem. Existing approaches for particle picking are either slow or are limited to picking a few particles of interest, which requires large annotated and difficult to obtain training datasets. In this work, we propose ProPicker, a fast and universal particle picker that can detect particles beyond those included in the training set and can process tomograms within a few minutes. Our promptable design allows for selectively detecting a specific protein in the volume based on an input prompt. Our experiments demonstrate that ProPicker can achieve performance on par with state-of-the-art universal pickers, while being up to an order of magnitude faster across a range of particles. Moreover, we show that ProPicker can be efficiently adapted to new proteins by fine-tuning on a handful of annotated samples. Code and model weights will be released upon publication.