Witnesses said the attackers targeted a hotel in the town before escaping the scene.
Five wounded people were taken to hospital, according to the Kenyan Red Cross.
Kenya has suffered a series of attacks since its troops moved into southern Somalia to combat Islamist al-Shabab militants in 2011.
Police confirmed that an operation was under way to identify the assailants.
The town has seen several such attacks in recent months. In January, another shooting in Garissa killed five people and wounded another four.
In October, gunmen shot dead a police officer and wounded another in Garissa. In November, three Kenyan soldiers and two police were shot dead there.
Attacks blamed on al-Shabab have previously sparked retaliatory violence against the country’s Somali population.
In November, riots broke out in the capital Nairobi as angry youths blamed ethnic Somalis for a deadly explosion.
Xafiiska Wararka Midnimo, email@example.com