Gracie-May Rogers was last seen with her mother Kelly Gibson, aged 35, at about 10.00 BST on Tuesday.
It is believed they boarded a plane from Glasgow airport at 5.30pm on Wednesday, along with Gracie’s father Lee Rogers, aged 39.
Officers think they arrived in Alicante, Spain, at 21.35 BST on the same day, although there have been no confirmed sightings of them in Spain.
Lancashire Police said they are treating Gracie-May as a missing child and her parents, Kelly Gibson and Lee Rogers, are now wanted on suspicion of child abduction.
In a statement, the force said they are “working closely” with their law enforcement and child protection partners in Spain to “bring Gracie-May home safely”.
Detective Inspector Andy Ellis, of Lancaster CID, said: “We are growing increasingly concerned, especially for the welfare of Gracie-May and Kelly Gibson, and we would appeal to anyone who sees the three of them together or separately to get in touch urgently.”
Police said the last information they have is that the family landed in Alicante but the family could have moved to another location.
Det Insp Ellis added: “We appreciate that this incident may cause concern for some people but we are working closely with our partners in the Spanish Police and our overriding priority is the safe return of this young child.”
Anyone with relevant information has been urged to call Lancashire Police on 101 quoting log 0621 of 25 August.
Those who see the family should contact local police in the relevant area.