The army said in a statement that the attempt by some 150 protesters to interfere with the vote "compelled" the soldiers to open fire in Dang, 200 kilometers (125 miles) southwest of Katmandu.
Two of the protesters were injured at the scene, and one died later at a hospital, the army said.
Attempts to reach Dang by telephone and verify the army's account were unsuccessful because phones were not working in the area. It was unclear if the government had cut communications.
Authorities had threatened on the eve of the vote to shoot anyone caught trying to disrupt the elections, as the rebels and nearly every major political party had pledged to do.
The vote was seen as a test of King Gyanendra a year after he seized power, but were marred by low turnout and a rebel attack that killed two people hours before polls opened.
There were frequent protests in the weeks before the elections, which the opposition boycotted, calling them a sham intended to legitimize King Gyanendra's rule, reports the AP.