The baby was attacked at a family member’s home in Thorpe Pyn Croft, Dalton, Huddersfield on Sunday.
He later underwent surgery at Leeds General Infirmary for a fractured jaw and facial lacerations.
A spokesperson from the West yorkshire Poice said: “Enquiries are continuing into the breed of the dog, it may have to be put down if it is a pit bull terrier
“The baby continues to be treated for serious but not life threatening injuries”
The hot weather is being considered as one of the possible reasons for the attack.