The 22-year-old, who broke his hand in April, has been diagnosed with a "partial stress fracture of the lumbar spine".
"I was completely devastated to hear the news of my stress-related back injury," Topley told the club's website. "I just want to play for Hampshire and contribute to their cricket.
"Last week, I was particular concerned that my 2016 season was going to be limited to one single session, on the very first day of the season, when I fractured my hand batting. It is hoped that I may be back bowling in August so hopefully I will have the opportunity to repay Hampshire for the faith they have shown in me."
Topley joined the county at the end of the 2015 season.