The youngster was injured after a fight broke out as crowds gathered to watch the annual County Grand Orange Order parade at Glasgow Green on Saturday.
A number of people were involved in the disturbance, which resulted in the girl being struck with what is believed to have been a bottle.
A 22-year-old woman with the girl was also injured.
Police are now appealing for anyone who may have witnessed the disturbance to check their mobile phones or cameras. Email GlasgowGreenAppeal@scotland.pnn.police.uk.