Sudairi, currently deputy CEO, will take over from Shiha on Nov. 16. Shiha is leaving for personal reasons after more than four years in the post.
The firm is the main electricity producer in the kingdom with an 81.2 percent indirect government ownership.
On Monday, local media reported that a huge fire broke out at a power plant in central Riyadh. The company said in a statement that it had to isolate the station in order to extinguish the fire, causing a partial shutdown in some neighbouring areas.
In September, Reuters reported that Saudi Electricity is set to issue $2 billion in sukuk, or Islamic bonds.