Bumrah, the 2024 international cricketer of the year, has been out action since he missed the final day of the fifth Test against Australia in Sydney in January because of a back injury.
Five-time champions Mumbai announced Bumrah's return with a video on social media titled "ready to roar".
Bumrah, 31, will be key to Mumbai's hopes of a turnaround after losing three of their four matches this season.
They face Bengaluru at their home Wankhede Stadium on Monday.