Guard Disarms Knifeman After Stabbing in Leicester Square
The 29-year-old Abdullah claimed to have "heard a scream" and "jumped on" the man who was assaulting the youngster, held him down and removing the knife.
"I attempted to help a child who I just seen being stabbed. I just have to preserve them," he murmured.
Abdullah claimed that within four minutes of the incident on Monday morning, he and his colleagues had administered first aid to the child before the police had up.
The Metropolitan Police said the girl will require hospital treatment but her injuries are not life threatening, while her mother suffered minor injuries.
The force said a 32-year-old man was arrested at the scene and officers are not looking for anyone else in connection with the attack.
There is no suggestion the incident is terror-related and police don't believe the suspect and the victims are known to each other.
Abdullah, who has worked at the TWG Tea shop for around eight months, said he "heard a scream" and saw there was a person in his early to mid-30s "stabbing a kid".
"I jumped on him, held the hand in which he was [carrying] a knife, and just put him down on the floor and just held him and took the knife away from him," he said.
"Then a couple of more people joined as well, and we just held him until the police came, it took maybe three to four minutes for the police to arrive and then they just took him into custody."
Police praised the bravery of those who stepped in to help.
"This is a horrific incident and our thoughts are with the victims and their family," said Detective Chief Superintendent Christina Jessah.
"We will continue to provide support to them over the coming days and weeks.
"I would like to pay tribute to the members of the public, including staff from local businesses, who bravely intervened in this incident.
"They put themselves at risk and showed the best of London in doing so."