Officials said about 26 had so far been captured since the quake at 20:46 local time on Tuesday.
Chile’s President Michelle Bachelet has declared disaster areas in the northern regions of Arica and Parinacota and Tarapaca, and will visit them later.
At least six people are known to have died and tens of thousands evacuated.
There have been power cuts, fires and landslides as dozens of aftershocks – including a 6.2 tremor – continued through the night.
But although waves of up to about 6ft hit some areas tsunami warnings in several areas have now been lifted.
It was not clear exactly how the women inmates escaped from the prison in Iquique.
But Interior Minister Rodrigo Penailillo said a military plane of 100 anti-riot police was being flown to work alongside 300 soldiers already operating in the city.
They will be tracking down the prisoners as well as preventing “looting and disorder”, Chilean authorities said.
The quake struck about 52 miles north-west of Iquique, a mining area.
The tremors set off landslides that blocked roads, hit power supplies, damaged a number of homes and caused fires in some businesses.
Officials said the dead included people who were crushed by collapsing walls or died of heart attacks.
Iquique Governor Gonzalo Prieto told local media that in addition to those who died, several people had been seriously injured.
The tsunami alert sent tens of thousands fleeing coastal areas of Chile. Television pictures showed traffic jams as people tried to head for safer areas.
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