The planned protest follows a massive rally last November galvanised by the beheadings of a group of Hazaras, which became a symbol of the broader public discontent with President Ashraf Ghani's regime.
The TUTAP power line, which would connect the energy-rich Central Asian nations of Turkmenistan, Uzbekistan and Tajikistan with Afghanistan and Pakistan, is regarded a crucial project in the electricity-starved region.
But it has been mired in controversy, with leaders from the minority group demanding that the line be routed through central Bamiyan province, which has a large Hazara population.
Hazara leaders in the ethnically divisive nation lashed out at the Pashtun president, saying the decision to reroute the line was a sign of discrimination.
"People will pour into Kabul's streets to stage a massive protest before marching towards the presidential palace," Hazara lawmaker Arif Rahmani told AFP.
"We want the power line to cross through Bamiyan, which has seen no development in 15 years. We are demanding justice, not charity."
"Staging peaceful protests is the civil right of every Afghan citizen... We respectfully request that our countrymen not allow the enemy (to) misuse this opportunity and disrupt public security," the interior ministry said in a statement.
The dispute, which highlights the challenges of modernising the war-torn country, threatens to overshadow TUTAP which could help ease nationwide power blackouts.
Hazara protesters repeatedly heckled Ghani during an anti-corruption summit in London last week.
The president faces rising unpopularity amid endemic corruption, rampant unemployment and growing insecurity in Afghanistan.
