Police were called to an address in Hawick in the Scottish Borders at 4.35pm on Thursday.
The boy was taken to hospital and officers remain at the scene.
A police spokesman said: “About 4.35pm on Thursday April 11 2019, emergency services were called to an address in Hawick after a report of a baby being attacked by a dog.
“A baby boy has been taken to hospital where he remains in a critical condition.
“Officers remain in attendance and inquiries are ongoing.”