The two-time Masters champion, 38, carded a six-under-par 66, which included an eagle and five birdies, before play was suspended.
Five players are one shot behind Watson in China.
England's Tommy Fleetwood is three shots back after a three-under-par 69.
The 56 players who still have to finish their opening rounds will do so early on Friday before the second round takes place.
Shenzhen International leaderboard
American Bubba Watson has a one-shot clubhouse lead at the storm-interrupted Shenzhen International, with 56 players set to finish their first rounds early on Friday.