A nine-year-old Chelsea fan suffered a panic attack as a result of the flare.
The Football Association are also looking into the incident.
"The incident was reported to us at 5.40pm [17:40 BST], shortly after Liverpool scored their first goal, that a flare was thrown from the upper section of the Anfield [Road] Stand.
"Following this, at around 6.20pm [18:20 BST], officers received reports that a young Chelsea fan, believed to be nine years old, had been taken to the first-aid centre where he was treated by St John Ambulance staff after suffering a panic attack as a result of the flare.
"At this stage, it is not clear who threw the flare. However, investigations are ongoing."