The fire began at 08:30 local time (00:30 GMT) and was contained within two hours, Xinhua news agency quoted a local government official as saying.
Four children died in the fire, while three succumbed to their injuries on the way to hospital, it added.
The cause of the fire has yet to be determined.
Local residents say that a woman named Yuan Lihai had been using the house in Lankao county to shelter orphans and abandoned children, Xinhua reports.
Reports say that Ms Yuan, a street vendor, has provided shelter to dozens of children over two decades.
It remained unclear how many children were in the house during the incident and how many were injured.
Henan province has seen tragedies involving children in recent months. In December, a man wielding a knife wounded 23 children at a school in Chenpeng village.