Krishnamaya Mabo went missing from her family's terraced home in Arborfield Garrison in Berkshire on Sunday evening.
Her body was found in a field near Robin Hood Copse the following afternoon, the BBC reported.
The 30-year-old suspect, who was arrested in Reading, around 5 km from the scene of the attack, is being questioned today on suspicion of murdering Mabo.
"Magistrates this afternoon granted investigators a further 36 hours to keep him in custody," police said.
Police were called in to help search for Mabo after she was reported missing from her home in Arborfield on Sunday evening.
A police helicopter and uniformed officers initially failed to find any trace of her.
But during a renewed search the following afternoon, a police officer stumbled across the body in a field as he walked up the country lane.
The post-mortem examination at the Royal Berkshire Hospital on Tuesday revealed she was asphyxiated.
She was ambushed, dragged into a field and murdered by a stranger as she waked down a country-lane just 500 yards from her home, it emerged today.
The killer "followed her up country lane and pounced when out of sight", the police said.
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