The development of plasma-based accelerators has enabled the generation of very high brightness electron bunches of femtosecond duration, micrometer size and ultralow emittance, crucial for emerging applications including ultrafast detection in material science, laboratory-scale free-electron lasers and compact colliders for high-energy physics. The precise characterization of the initial bunch parameters is critical to the ability to manipulate the beam properties for downstream applications. Proper diagnostic of such ultra-short and high charge density laser-plasma accelerated bunches, however, remains very challenging. Here we address this challenge with a novel technique we name asfemtosecond ultrarelativistic electron microscopy, which utilizes an electron bunch from another laser-plasma accelerator as a probe. In contrast to conventional microscopy of using very low-energy electrons, the femtosecond duration and high electron energy of such a probe beam enable it to capture the ultra-intense space-charge fields of the investigated bunch and to reconstruct the charge distribution with very high spatiotemporal resolution, all in a single shot. In the experiment presented here we have used this technique to study the shape of a laser-plasma accelerated electron beam, its asymmetry due to the drive laser polarization, and its beam evolution as it exits the plasma. We anticipate that this method will significantly advance the understanding of complex beam-plasma dynamics and will also provide a powerful new tool for real-time optimization of plasma accelerators.