The attack at the family home in Eastry, near Dover in Kent, on Monday left the toddler in danger of losing an eye.
His parents are by his bedside and are said to be "devastated".
The attack, which only came to light on Thursday, is the latest in a recent spate of attacks by dogs on children.
'Severely attacked'
A spokesman for Kent Police said: "He is being treated at the Kent and Canterbury Hospital where the family are reluctant to go into details but he is said to be happy.
"He was quite severely attacked."
There are calls for pet owners to be licensed following the recent dog attacks.
On Sunday, Nicki Hughes, 10, became the second girl to be attacked in Wolverhampton in less than a fortnight.
Leah Preston, five, nearly died after being attacked in her garden in Wolverhampton by two bull mastiff cross-breeds on 16 May.
And on Monday night a six-year-old boy suffered serious face and neck injuries when he was savaged by a Japanese akita dog in a pub car park in the Shiregreen area of Sheffield.