The girl's father, brother and a cousin, who were all riding a motorbike, were injured in the incident.
The girl, along with those injured, was taken to the Punjab Social Security Hospital. The girl's brother was severely injured and had to undergo an operation.
Punjab Chief Minister Shahbaz Sharif has ordered an inquiry into the incident, Express News reported.
The Punjab Prohibition of Kite Flying (Amendment) Bill, 2009, forbids committing or abetting the act of kite flying and also the manufacture and sale of kites.
Many in Pakistan, especially in the Punjab province, love to fly kites and are known to lace the string with extra glass powder.