Amanda was last seen on 21 March
The 20-year-old woman from Tewkesbury, Gloucestershire, was arrested last Tuesday.
It followed complaints from the Dowlers that they had received hoax telephone calls at their home in Walton-on-Thames in Surrey.
Nothing has been seen of the Dowlers' 13-year-old daughter, known as Milly, since she disappeared walking home from the train station in Walton-on-Thames on 21 March.
A Surrey Police spokeswoman said on Monday a woman was arrested by Gloucestershire Police last Tuesday in connection with the hoax calls.
The spokeswoman said the woman had been released on police bail until 13 May.
'Nightmare and reality'
On the last day she was seen, Amanda shared a plate of chips with a friend before phoning her father, Robert, to say she was heading home - she never arrived.
Her best friend, Hannah Macdonald, says she is firmly convinced Amanda did not leave home voluntarily.
On the BBC's 4x4 television show on Monday she says: "You read a paper or you see the news and you think 'That is awful' then you forget about it - but now it has happened to my best friend.
"It is really hard to come to terms with it because it feels like a nightmare and I cannot tell the difference between the nightmare and the reality."
She adds: "I just think of all the good times that Milly and I had and I just think we will have them again.
"I just keep looking forward to having them again because Milly is such fun."
A body found on 23 April in the River Thames a few miles downriver from where Amanda disappeared proved to be that of a woman in her seventies.
Maisie Thomas, 73, went missing from Shepperton after going out for an early morning walk near the Thames on 14 March 2001.