He remains in custody and is expected to appear at Greenock sheriff court on Friday.
Schoolgirl Alesha MacPhail was reported missing from her grandparents' home in Rothesay, the island's main town, at 6.25am on Monday.
She said: "I understand that there will be a high level of concern among people living in this close knit community but I want to reassure people that everything possible is being done".
Detective Superintendent Stuart Houston praised Alesha's family for their "bravery" and the local community for "their support".
Her body was discovered a few hours later by a member of the public in woodland on the site of an abandoned hotel, reportedly around a mile from where her family reported she had vanished.
Late on Tuesday, Scottish police confirmed that six-year-old Alesha had been murdered and that, as a precaution, told islanders to "look out for each other and please look out for your families and the security and safety of your homes".
At the time of her disappearance, Alesha was staying with her grandmother as she celebrated the first days of a three-week summer break, BBC reports.
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Police said that some items had been removed, including a vehicle, as part of their investigations.
Officers are appealing to anyone who may have been in the area on the night/morning in question to come forward and contact them.
Kirsty Wallace, who lives on Bute, added: "Our island dont need you spouting rubbish". Bute is one of these places that is incredibly safe.
Wendy Davie, Alesha's head teacher at Chapelside primary school in Airdrie, about 60 miles away from Bute, said in a statement that Alesha "loved being at school and enjoyed all aspects of literacy, in particular writing".
Alesha's uncle CJ MacPhail wrote a tribute to the youngster on Facebook, thanking people for their support, local media reported. "She was such a perfectionist in her handwriting and was very proud of her work".
He wrote, "I would also like to let yous see what sort of lovely wee girl my niece was and also what whoever has done this has taken from us".
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