A child found badly injured in the Southland town of Otautau is now being treated at Auckland's Starship Hospital.

They remain in a critical condition at the children’s hospital on Tuesday.

A 19-year-old man and woman appeared in an Invercargill court on Monday, charged with wounding with intent to cause grievous bodily harm.

Their names were suppressed and they were remanded in custody until October 6.

Crown prosecutor Mary-Jane Thomas told the court the child was unlikely to recover.