A stray bullet wounded a child when the militants attacked Kamuthe primary school, in Garissa County, a police report seen by Reuters said. The militants also destroyed a telecommunications mast in the attack in the early hours of Monday, the report said.
The al Qaeda ally has targeted Kenya in frequent attacks, part of a retaliation campaign against the country for sending troops into Somalia in 2011 after a series of cross-border raids and kidnappings.
The group has stepped up the pace of its attacks in Kenya since the New Year.
Somalia and Kenya have porous borders and often ad hoc methods for sharing intelligence.
Last week, four schoolchildren were killed during a gunfight between the Somali militant group and local police in Garissa. The attackers targeted a telecommunications mast in that assault as well.
The United States bolstered its presence in Kenya last week after al Shabaab killed three Americans in an attack on a military base used by U.S and Kenyan forces.
Al Qaeda-affiliated al Shabaab has waged an insurgency in Somalia since 2008, aiming to topple the government and impose its own strict interpretation of sharia, or Islamic law.
Last month, at least 90 people were killed in a bombing in Somalia's capital Mogadishu in the country's deadliest attack in more than two years.
Al Shabaab militants on Sunday shot four men in a public execution in a region south of the Somali capital Mogadishu, an official from the group told Reuters on Monday.
The four men were accused of spying for the Somali government and military, said Mohamed Abu Usama, al Shabaab’s governor for the Lower Shabelle region.
(Reporting by Humphrey Malalo; Additional reporting by Feisal Omar in Mogadishu; Writing by Omar Mohammed; Editing by Maggie Fick, Alex Richardson and Peter Graff)