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
David Cameron has been urged to visit Calais to witness the impact of the migrant crisis "first-hand".
The cost of filling up an average diesel car has dropped by £3 in just a month, new figures have shown.
Singer Gwen Stefani and her British husband Gavin Rossdale are to divorce after almost 13 years of marriage.