Markram was the front-runner for the job after leading SRH's sister franchise, Sunrisers Eastern Cape, to the inaugural SA20 title in Johannesburg recently.
The Jammu and Kashmir all-rounder was picked by Sunrisers Hyderabad for Rs 2.6 crore.
Earlier this month, former all-rounder Moody stepped down as the head coach of Indian Premier League team Sunrisers Hyderabad.
This will be the 53-year-old's maiden assignment as a head coach of a T20 team.
Malik has the ability to bowl fast and that too with an aggression that is rarely seen among Indian pacemen.
For SRH, Fazalhaq Farooqi took two wickets for 32 runs.
Williamson struggled big time this IPL season, scoring just 216 runs from 13 matches.
Mumbai Indians were restricted to 190/7 in response to the Sunrisers total of 193/6.
Andre Russell who scored an unbeaten 49, bagged 3/22 later.
SRH were all out for 125 in 19.2 overs, with leggie Wanindu Hasaranga picking up 5/18.