The quake, which stuck at 2.09am had its epicentre nine kilometres from Saxon at a depth of around seven kilometres below ground.
The seismic event was felt across Lower Valais, especially around the towns of Fully, Martigny and Aigles, the SED said in a statement.
The service said it had received 200 calls from people who had felt the quake in the minutes after the quake.
The area of Saxon has already experience seismic activity this year: in February, a quake measuring 2.6 on the Richter scale was felt in the zone.
Wallis has experienced numerous small quakes in recent years, not uncommon in the canton which has the highest earthquake activity in Switzerland.
02:09 earthquake with a magnitude of about 3.2 near Ovronnaz VS. May be perceptible. No damage likely. https://t.co/mQpnlAn9z7— SeismologicalService (@seismoCH_E) August 23, 2018
Around ten quakes of between 3 and 4 magnitude hit the country every year, with a 4+ quake expected every 1–3 years.