The country plans to hand over command of the northern Faryab province to Afghan security forces by the summer of 2012 and expects to withdraw its contingent from the provincial capital Maimana a year later, the minister said.
"It will not be a dramatic transfer done overnight," he told public broadcaster NRK during a visit to Afghanistan's northern capital Mazar-i-Sharif where other Norwegian troops are stationed.
Norway currently has some 500 troops in Afghanistan, including more than 300 tasked with security missions in Faryab while the remainder work with command and logistical issues in Mazar-i-Sharif and Kabul.
"After the withdrawal, some soldiers will remain in Mazar-i-Sharif to train and advise" the Afghan forces, Barth Eide told Norwegian news agency NTB.
The announcement came as an international conference opened in Bonn on the future of Afghanistan after the departure of NATO forces at the end of 2014.
Ten Norwegian soldiers have been killed in Afghanistan since international forces invaded in late 2001 to remove the Taliban regime.