Police used tear gas on the protesters and smoke could be seen rising from the area.
The Islamic Movement of Nigeria (IMN), a group that represents Nigeria's minority Shia Muslims, tried to enter the complex, sparking the confrontation with police.
IMN members protest regularly outside the National Assembly in the capital, Abuja, calling for the release of their leader, Ibrahim el-Zakzaky, who has been in detention since 2015.
According to Bafar, a 24-year-old student who was at the protest, trouble began when the group insisted on gaining access to the National Assembly premises to present their grievances to federal legislators.
"The security ... took our report to go and give the legislators but perhaps they refused to inform the legislators, or the legislators refused to respond. So, we decided to enter and submit it ourselves," Bafar, who gave only his first name for security reasons, told Al Jazeera.
"But they refused us and started spraying tear gas and shooting live bullets sporadically. I saw more than three people collapsing," he said.
Police said they had arrested 40 protesters during Tuesday's incident. The assembly remained on lockdown as of late afternoon.
Both sides blamed the other for the shooting. Police said officers had "used minimum force to disperse the unruly protesters."
In a statement, police said two officers were shot and wounded in the legs, and six other officers were injured by individuals using clubs and stones.