Little is known about the internal properties of Callisto-the outermost of Jupiter’s four large galilean moons-other than the average density (about 1.8 cm(-3)). The recent unexpected discovery(1-4) that Ganymede, and perhaps Io, has an internally generated magnetic field, combined with gravity results(5,6) suggesting that both Ganymede and Io are internally differentiated with metallic cores and rocky mantles, has heightened anticipation of the results obtained by the Galileo spacecraft in its recent fly-by of Callisto. Here we report that the spacecraft, passing the moon at a distance of only similar to 1,100 km from the surface, detected only a small enhancement of the field strength (similar to 7 nT), which may be related to changes in the jovian plasma environment caused by Callisto(7). Callisto does not have an internally generated magnetic field.