Police gave no reason for the attack.
The government blamed militants from the restive far-western region of Xinjiang for both those attacks.
Guangzhou police "arrived quickly on the scene" on Tuesday and shot one of the attackers. The official Nanfang Daily said another suspect had been caught by police after fleeing the scene.
"After verbal warnings were ineffective, police fired, hitting one male suspect holding a knife, and subdued him," Guangzhou police said on an official microblog.
They did not identify the attackers.
Provincial television showed pictures of what it said was an apparently injured suspect being pressed to the ground by police and plain-clothed security, as they removed a bloodied white t-shirt.
It was not possible to see the person's face.
City newspaper the Guangzhou Journal wrote on its microblog that the attackers carried half-meter (20-inch) knives, wore white clothes, including white hats, and launched their assault as passengers were leaving the station.
Some other reports on Chinese media outlets' microblogs said there were four attackers in total.
The official Guangzhou Daily, citing a store owner who witnessed the violence, said the suspects squatted on the ground next to his shop for about two hours, covering their baggage with clothing.
They suddenly let out a shout, pulled out knives from their bags, and began attacking people, it said on its microblog. Police were on the scene within on minute and began firing warning shots, it added.
Photos circulated online in state media showed police cordoning off an empty plaza. There was an ambulance parked there and spots of blood on the ground.
China blamed religious extremists for a bomb and knife attack at a train station in Urumqi, regional capital of Xinjiang, last Wednesday that killed one bystander and wounded 79.
The government called the attackers "terrorists", a term it uses to describe Islamist militants and separatists in Xinjiang who have waged a sometimes violent campaign for an independent East Turkestan state.