Block has become the latest prominent object of criticism by Hindenburg, whose business revolves around publishing research reports that harshly evaluate companies — and then, often, betting that their shares will fall, a practice known as short selling.

A Hindenburg report erased billions of dollars in market value from the Adani Group, the industrial conglomerate founded by the Indian billionaire Gautam Adani. Hindenburg’s allegations of fraud at the electric-truck maker Nikola eventually led to the ouster — and criminal prosecution — of Trevor Milton, the company’s chief executive.

Block, which was known as Square until late 2021, was founded by Mr. Dorsey and Jim McKelvey in 2009. Begun as a platform for merchants to take card payments, it eventually added Cash App and, through takeovers, the buy-now-pay-later platform Afterpay and the streaming music service Tidal.

In its report, Hindenburg wrote that Block’s Cash App platform was rife with fake accounts that artificially bolstered its user counts. Of more concern is what the short seller said was prolific criminal activity on Cash App, including payments for illegal drug sales and sex trafficking. (Unusually, Hindenburg cited as evidence several rap lyrics describing the use of Cash App to pay for drugs or assassination attempts.)

The investment firm also cited statistics from state governments including Massachusetts and Ohio suggesting that Cash App was used for fraudulent pandemic relief applications at a higher rate than other banking services. The report also accused Block executives of ignoring warnings by employees and regulators about signs of potential pandemic relief fraud.