In the field of X-ray microcomputed tomography (μCT) there is a growing need to reduce acquisition times at high spatial resolution (approximate micrometers) to facilitate in vivo and high-throughput operations. The state of the art represented by synchrotron light sources is not practical for certain applications, and therefore the development of high-brightness laboratory-scale sources is crucial. We present here imaging of a fixed embryonic mouse sample using a compact laser-plasma-based X-ray light source and compare the results to images obtained using a commercial X-ray μCT scanner. The radiation is generated by the betatron motion of electrons inside a dilute and transient plasma, which circumvents the flux limitations imposed by the solid or liquid anodes used in conventional electron-impact X-ray tubes. This X-ray source is pulsed (duration <30 fs), bright (>1010 photons per pulse), small (diameter <1 μm), and has a critical energy >15 keV. Stable X-ray performance enabled tomographic imaging of equivalent quality to that of the μCT scanner, an important confirmation of the suitability of the laser-driven source for applications. The X-ray flux achievable with this approach scales with the laser repetition rate without compromising the source size, which will allow the recording of high-resolution μCT scans in minutes.