Police were called to an address on Frank Street, in the Little Horton area of Bradford, at 7.26pm yesterday and had to shoot the animal so paramedics could treat the boy.
A West Yorkshire Police spokesman said:
The child was then taken to Leeds General Infirmary where his condition this morning is described as stable, with injuries which are not believed to be life-threatening.
Inquiries are now ongoing as to the breed of the dog and to establish whether any criminal offence has been committed.
More top news
Former Conservative party chairman says the mistakes of two Tory Prime Ministers in row have had "calamitous" consequences for Britain.
A 42-year-old woman has been held after at least six people were injured in a collision with a car outside a sports centre in Newcastle.
The Brexit Secretary's comments come after Chancellor Philip Hammond's remarks that no EU deal would "very, very bad" for the UK.