The "Sherlock" star's wife is said to have given birth earlier in March to a boy, who has been named after Shakespearean hero Hal.
Prince Hal was the nickname, the great writer gave to the young Henry V in his plays.
Cumberbatch also starred in "The Hollow Crown", a BBC series based on Shakespeare's work.
The couple, who tied the knot in 2015, is also parents to Christopher, who was born in June same year.