Austrian Wiesberger hit a seven-under-par 65 to move into a four-stroke lead over Denmark's Thorbjorn Olesen and South African Dylan Frittelli.
Like Olesen and Frittelli, Scotsman Ramsay had a four-under-par 68.
First-round leader Bubba Watson was tied with Ramsay but had his second round suspended after five holes.
By that time, the American two-time Masters winner had improved by one shot after his opening 66 at Genzon Golf Club in China.
Half the field had yet to complete their second 18 by the time play came to a halt because of lightning and heavy rain.
The second round will resume on Saturday, with the third round now due to follow off two tees.
Scotland's Scott Jamieson and England's Jordan Smith were among those to have finished their round and lie in a tie for seventh after second-successive 69s.
Duncan Stewart and England's James Morrison lie two strokes further back, the Scot having picked up three strokes in the eight holes he managed to complete.
After his bogey-free round, Wiesberger told the European Tour website: "It was a long day. I got up at 04:30 to finish a couple of holes.
"I played a few holes on Tuesday and I said to my caddie it feels like a course that suits me and suits my game."
Shenzhen International leaderboard
Richie Ramsay is in a tie for fourth place, five strokes behind leader Bernd Wiesberger, after his second round at the storm-hit Shenzhen International.