The body of the schoolgirl was found in woodland on the site of a derelict hotel on Monday morning, around two-and-a-half hours after she was reported missing from her grandmother’s home.
The police said the man they arrested was under the age of 18.
Following the results of a post-mortem examination on Tuesday evening, police confirmed they were treating the six-year-old’s death as murder, although they have not revealed the cause of death.
On Wednesday night, senior investigating officer, Detective Superintendent Stuart Houston, said: “The response to our earlier public appeals has been significant. However, despite this evening’s major development, I am still appealing for anyone who was in the Ardbeg Road area of Bute on Sunday night or in the early hours of Monday and who may have information about Alesha’s death to contact us.
“Anyone who has CCTV at their home or business, or indeed any motorists with dashcam footage which might help with our investigation are also urged to get in touch.”
There was increased police activity yesterday at the property where Alesha had been staying. More than a dozen officers entered the garden of the Ardbeg Road property with long sticks to search the gardens and bushes surrounding the building.
A Police Scotland spokesman confirmed a number of items, including a vehicle, have been recovered as part of the investigation.
The car is believed to have been removed by officers on Monday or Tuesday.
The force spokesman added: “The response from the public following our appeals has been very good and we would like to thank those who have taken the time to contact us with information so far. A number of lines of inquiry are being followed up, however we continue to appeal to those who have not yet spoken to police and may have information to get in contact with us.
“We would like to speak to anyone who may have CCTV at their home or business or any motorists who have dashcam footage which might help with our investigation.”
The island community has been left in shock by the murder of the six-year-old, who was a few days into a three-week break to visit family.
Reverend Owain Jones has opened his United Church of Bute in Rothesay to allow people to visit at any time.
He said: “We’re all absolutely staggered, we have no words for this and it’s beyond any power of words to express.
“We’re all just really sitting in a kind of shared stunned silence just trying to uphold each other. Bute is one of these places that is incredibly safe, you take all sorts of things for granted here and don’t panic if you forget to lock the house or whatever.
“It’s not a remote island in the classic sense – it’s only 90 minutes to Glasgow – but even so it is an island and we all know each other at least by sight, and it’s an extremely safe place and there is no context for this.”
Meanwhile, DS Houston said Alesha’s family are “utterly devastated” at her death, and he appealed for anyone with information to come forward.
He is still keen to speak to people who were involved in the search for the missing girl early on Monday morning.
He added: “Alesha had lots of friends who will no doubt find it very difficult to comprehend why they will never see their friend again. For such a young girl to have her life taken away is incomprehensible.”
Flowers, teddies and balloons have been left on the pavement outside the property on Ardbeg Road, with messages attached reading “sleep tight little angel” and “good night little angel”.