Dust is common close to the martian surface, but no known process can lift appreciable concentrations of particles to altitudes above ~150 kilometers. We present observations of dust at altitudes ranging from 150 to above 1000 kilometers by the Langmuir Probe and Wave instrument on the Mars Atmosphere and Volatile Evolution spacecraft. Based on its distribution, we interpret this dust to be interplanetary in origin. A comparison with laboratory measurements indicates that the dust grain size ranges from 1 to 12 micrometers, assuming a typical grain velocity of ~18 kilometers per second. These direct observations of dust entering the martian atmosphere improve our understanding of the sources, sinks, and transport of interplanetary dust throughout the inner solar system and the associated impacts on Mars's atmosphere.