Attempts to cut down China’s debt problems aren’t working, so Beijing is casting a wider net. Whether it works or not, the move adds to the sense that monetary tightening is in the air.

In a document sent out this month and widely published Wednesday, China’s central bank tightened the noose once again on banks use of wealth-management products—investment vehicles sold to customers that are typically stashed off-balance sheet to avoid banks’ breaching regulatory capital limits.

The...