Keir Starmer said that under a "mandatory reporting" law, those who failed to act could be sent to jail following claims that schools and hospitals are not doing enough to protect children from abuse.
While statutory guidance has been issued previously urging professionals such as teachers, doctors and social workers to report child abuse, failure to do so is not a crime.
Mr Starmer, who was succeeded as director of public prosecutions by Alison Saunders on Friday, said it was time to "plug a gap in the law" that had "been there for a very, very long time".
'Ought to do something about it'
"It's a very simple proposition. If you're in a position of authority or responsibility in relation to children, and you have cause to believe that a child has been abused, or is about to be abused, you really ought to do something about it," he said.
"There are just too many examples of cases where those who have suspected abuse have not really done anything about it and the perpetrator has either got away with it or, worse still, been able to perpetuate the offending."
No evidence to show it is better
However, the government said mandatory reporting was not the answer.
A Department of Education spokesperson said: "Professionals should refer immediately to social care when they are concerned about a child.
"This happens every year in many thousands of cases and numbers of referrals have increased over recent years. Other countries have tried mandatory reporting and there is no evidence to show that it is a better system for protecting children."