The U.S. Department of State said on its website that this included up to $6 million for information on Abu Ubaidah, the al Shabaab leader who took command in September 2014 after his predecessor, Ahmed Godane, was killed by a U.S. missile strike.
The United States, other Western powers and countries in the region see the fight against the al Qaeda-aligned group as a vital part of the battle to prevent Islamist militancy spreading in East Africa and beyond.
Under the Rewards for Justice programme, up to $5 million was also offered for information on three other commanders, including Mahad Karate, also known as Abdirahman Mohamed Warsame, who is accused of playing a major role in the Garissa university attack in Kenya in April that killed almost 150 people.
The two others, Maalim Daud and Hassan Afgooye, were behind activities, such as training, recruiting and financing for the group, the State Department said.
Al Shabaab ruled Somalia for several years until 2011, when its forces were driven out of the capital Mogadishu by African Union troops. Since then, it has lost most of its main strongholds but still controls swathes of countryside and still launches attacks.
Among its most high-profile assaults was a raid on Westgate shopping mall in Kenya's capital Nairobi in September 2013, that left 67 people dead. It also launched attacks in 2010 in Uganda, which, like Kenya, has troops in Somalia fighting the group.
The U.S. programme offered up to $3 million each for information on two other senior figures in the group.
The U.S. State Department has offered rewards for other al Shabaab leaders in the past under its Rewards for Justice programme.
The programme, launched in 1984, has paid more than $125 million to more than 80 individuals who provided "actionable information that put terrorists behind bars or prevented acts of international terrorism worldwide", the State Department said. (Writing by Edmund Blair; Editing by Drazen Jorgic and Louise Ireland)