The Mariner IV spacecraft on 14-15 July 1965 passed within 9850 kilometers of Mars, carrying a solid-state charged-particle telescope which could detect electrons greater than 40 kiloelectron volts and protons greater than 1 million electron volts. The trajectory could have passed through a bow shock, a transition region, and a magnetospheric boundary where particles could be stably trapped for a wide range of Martian magnetic moments. No evidence of charged-particle radiation was found in any of these regions. In view of these results, an upper limit is established for the Martian magnetic moment provided it is assumed that the same physical processes leading to acceleration and trapping of electrons in Earth's magnetic field would be found in a Martian magnetic field. On this basis, the upper limit for the Martian magnetic moment is 0.1 percent that of Earth for a wide range of postulated orientations with respect to the rotational axis of Mars. The implications of these results for the physical and biological environment of Mars are briefly discussed.