The suspects were arrested on Tuesday night, after an arm and two legs were found in Loughborough, Leicestershire.
Police say they believe they know the identity of the victim, but are waiting to speak to his relatives.
It is thought he was killed during the weekend.
Three bags
The two men, aged 19 and 26, and the girl are being held at separate police stations.
On Sunday, a human arm wrapped in a carrier bag was recovered from the Grand Union Canal.
Police originally believed the remains to be that of a girl, but later confirmed the victim was male.
Police later uncovered two legs in another bag in Alan Moss Road.
The contents of a third bag found near playing fields in Rosebery Street have not been revealed.
House-to-house inquiries and extensive searches of the sites took place on Tuesday, prior to the arrests.
Shoe size
A spokesman for Leicestershire Police said detectives are still keen to hear from anyone who can help with inquiries.
Home Office pathologists confirmed that the victim was male.
It is thought that the child was around 5ft 5ins to 5ft 11ins and took a size seven shoe.
His ethnic origin is not yet known, but Home Office pathologists said he was probably not North African or Afro Caribbean.
Anyone with any information is asked to contact Leicestershire Police on 0116 222 2222.
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