The attack took place in the Puerto Santander municipality located in the troubled Norte de Santander department.
BACKGROUND: FARC rebels sabotages oil infrastructure in northern Colombia
The wounded were taken to a nearby hospital.
Authorities said the attack had to do with territorial disputes between local armed gangs who are competing for control along the Venezuelan border.
This is the fifth grenade explosion in Cucuta in just 15 days, reported radio station Caracol.