Phuket residents Phatcharee Boontaley, 35, and daughter Pitchaya Saekin, 11, are being treated at Bangkok Phuket Hospital after being hurt when a fan tipped over and caused rows of paint tins to topple along with the shelves.
The girl's father, Paiboon Seakin, 42, also suffered minor injuries.
The store has been closed temporarily while emergency crews work to clear the wreckage and investigate the cause of the collapse.
Central Group will cover all medical expenses of the injured, a spokesperson for the retailer said.
Following the incident, staff at all properties operated by Central Group have been ordered to thoroughly check the safety of shelves to avoid any similar incidents.
The incident is unprecedented. Nothing like this has ever happened at any properties operated by the Central Group, the spokesperson said.