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
Campaigners have hailed new tough guidance for prosecutors and police when tackling rape allegations as a "significant step forward".
The parents of Dylan Seabridge, from Pembrokeshire, said they believed their son was suffering from growing pains.
Andy Murray has defended fiancee Kim Sears over what appeared to be an expletive-laden rant towards opponent Tomas Berdych