The offer came after a cabinet-level meeting of the government Wednesday, and days after a U.S. airstrike targeting al-Shabaab leader Ahmed Abdi Godane.
"We will create a better livelihood...for those who meet the deadline," Khalif Ahmed Ereg, Somalia's security minister said of the amnesty, mentioning an opportunity for militants to "rebuild their future" in Somalia.
The Islamist militant group, which has ties to al-Qaida, controls much of the country and has launched frequent attacks on the capital, Mogadishu, and surrounding countries.
The fate of Godane, also known as Muktar Abu Zubair, remains unclear.
"The first news I got was that the emir was wounded, but I cannot say yet if he is dead or alive," an al-Shabaab spokesman said.
Godane claimed responsibility for the September 2013 attack on a Nairobi, Kenya, shopping mall in which nearly 70 people were killed.