Five other protesters were injured Sunday as police tried to disperse a group of people who barricaded a road in Mityana, about 60 kilometers (37 miles) from the capital Kampala.
The area’s representative in parliament, Francis Zaake, is hospitalized in critical condition.
Police said the officer who fired his weapon would be apprehended.
There were riots on Thursday in Kampala over the detention of another lawmaker, the pop star Kyagulanyi Ssentamu.
Both Zaake and Ssentamu were arrested for their alleged roles in an incident Monday in which the president’s motorcade was pelted with stones.
Ssentamu, who is detained in a military barracks, charged he was “severely tortured.”