Williamson led SRH in 13 games this season.
Taking to Twitter, SRH wrote: "Our skipper Kane Williamson is flying back to New Zealand, to usher in the latest addition to his family. Here's everyone at the #Riser camp wishing Kane Williamson and his wife a safe delivery and a lot of happiness!"
Williamson is departing for his homeland a day after leading SRH to a narrow three-run victory over Mumbai Indians (MI) to keep their IPL 2022 playoffs hopes alive.
Kane Williamson had a tough time as a batter in the ongoing IPL. He featured in 13 games, scoring only 216 runs at an average of 19.64 and a strike rate of 93.50.
On the other hand, his team SRH had an erratic campaign. They started with two back-to-back defeats and then won five successive matches before suffering five consecutive losses.
The Sunrisers are currently occupying the eighth spot on the points table, with 12 points from 13 matches. They will face Punjab Kings in their last league match on May 22.