The UK Government's warning follows the controversy surrounding the "internet twins" who were bought in the US by Alan and Judith Kilshaw.
The girls are now being looked after by Flintshire social services and the couple face a legal custody battle.
Under the 1976 Adoption Act, only local authorities and voluntary adoption agencies approved by the health secretary are allowed to advertise children for adoption.
Alert
Mr Hutton said the warning was intended to help the ISPs stay within the law.
"Recent High Court litigation in this country has confirmed that when an internet service provider becomes aware of illegal material on their server, they do need to take action to deal with that," he told BBC Radio 4's The World at One programme.
Mr Hutton denied the government was "shooting at anyone" in their haste to act following the Kilshaws' case.
"That is all we are trying to alert them to. We are not saying to all the UK ISPs that they must go away now and check all the material on their servers. That would be completely unreasonable and we are not unreasonable."
Mr Hutton said he expected the ISPs to take action if the health department, a local authority or member of the public reported they were carrying an illegal site.
Draft legislation to tighten up on inter-country adoption already exists but the government is speeding up its introduction.
The US twins Belinda and Kimberley were adopted by the Kilshaws in Arkansas, after they paid £8,000 to a broker.
But an American couple is disputing custody, saying they adopted the children first.
Internet Watch Foundation chief executive David Kerr said the Department of Health seems to have realised that there were some things outside its control.
"There is nothing that the department can do about websites that are legal in the country where they are hosted."