J.P. Morgan Chase & Co. capped ATM withdrawals at $1,000 per card daily for noncustomers—cracking down as people started pulling out tens of thousands of dollars at a time when the bank was modifying its machines to dispense hundred-dollar bills with no limit.

The bank said there doesn’t appear to be fraud involved. But partly due to heightened regulatory scrutiny, banks are paying more attention to large cash transfers that could be a sign of money laundering or other types of shady activity. Typically, the card-issuing...