The River Don, which flows past Meadowhall, is rising rapidly, leaving some fearing that it is at risk of breaching.
Meadowhall bosses say its flood defences have been deployed as a precautionary measure but the centre remains open.
The statement reads: “Due to the current weather conditions, we have taken the decision to deploy our flood defences as a precautionary measure and Meadowhall Drive is closed as a result.
"The centre remains open and we are closely following the latest updates from the Environment Agency.”
A number of flood alerts and warnings have been issued for Sheffield and Millhouses Park has been closed as a precaution.
More to follow.