The agency is seeking the arrest of Abdikadir Mohamed Abdikadir, better known as Ikrima, for his role in recruiting Kenyan youth into al-Shabaab and as a commander of a force of the group's Kenyan fighters in Somalia.
Jafar, aka Amar, is wanted for being Abdikadir's deputy, while Yasin Kilwe is described as Al Shabaab's emir for Puntland in northern Somalia.
In a statement, the department noted that Al Shabaab has killed thousands of civilians, aid workers and peacekeepers in Somalia, Uganda and Kenya since 2006.
It denounced two terror attacks launched by the group respectively in Kampala, Uganda in July 2010 and in Nairobi, Kenya in September 2013, in which over 70 people including one American citizen and more than 60 people were killed separately.
"Al Shabaab's terrorist activities pose a threat to the stability of East Africa and to the national security interests of the US," the department said.
Washington blacklisted the group as a foreign terrorist organisation in March 2008, which announced an alliance with Al Qaeda in February 2012.