The 55-year-old was taken to Cedars-Sinai Medical Center in Los Angeles on Monday, TMZ reported.
In a post on Instagram, he said: "I'm doing great and getting excellent care from my medical team."
He is "resting comfortably" after the aneurysm, his lawyer told Billboard.
In his post, Dr Dre also wrote: "I will be out of the hospital and back home soon. Shout out to all the great medical professionals at Cedars. One Love!!"
Friends and fellow stars have sent their well wishes after the reports of his ill health emerged.