It has not been confirmed whether the 26-year-old man also arrested on suspicion of attempted murder is the three-month-old boy"s father.
The tot was rushed to Gloucestershire Royal Hospital on Saturday at 11pm.
He was transferred to Bristol Children"s Hospital, where he remains in a critical condition.
Detectives have sealed off a council-owned flat in Archdeacon Street in Gloucester.
The pair have not been charged.
Gloucestershire Constabulary said: "Police were called to Gloucestershire Royal Hospital at 11am on Saturday July 30 after concerns were raised for
a baby"s welfare.
"A baby boy, aged three-months-old, was brought to the hospital with serious injuries.
"He now remains in a critical but stable condition
at Bristol Children"s Hospital.
"We wish to reassure the local community that this is thought to be an isolated and contained incident, with no wider risk to the public."
One resident, who wanted to remain anonymous, said: "We don"t know the family and I don"t think many people do.
"Around here it"s not a very close knit or neighbourly place, if I"m honest, but in this day and age where is?
"The family that lives there keep themselves to themselves.
"To be honest if it wasn"t for the police cars and police tape I don"t think any of us would have noticed anything had happened."
Local Tory councillor Pam Tracey said: "I just feel so sorry for that poor baby and I hope he is okay."