Police were contacted at about 01:00 BST on Tuesday after the baby had been admitted to Royal Blackburn Hospital.
The infant, who had been at a house in Infirmary Street, Blackburn, is in "a very poorly condition", a Lancashire Constabulary spokesman said.
A man, 21, and a 17-year-old girl, both from Blackburn, were held on suspicion of wounding with intent.
They have been bailed until 6 July.
The boy has been transferred to the Manchester Children's Hospital.
Two people have been arrested after a three-month-old boy was taken to hospital with a bleed to the brain.