“DFS is troubled to learn of potential discriminatory treatment in regards to credit limit decisions reportedly made by an algorithm of Apple Card, issued by Goldman Sachs, and the Department will be conducting an investigation to determine whether New York law was violated and ensure all consumers are treated equally regardless of sex,” the statement said.

An Apple spokeswoman directed questions to a Goldman Sachs spokesman, Andrew Williams, who said that the company could not comment publicly on individual customers.

“Our credit decisions are based on a customer’s creditworthiness and not on factors like gender, race, age, sexual orientation or any other basis prohibited by law,” Mr. Williams said.

Mr. Hansson did not respond to an interview request on Saturday night.

His wife’s experience with the Apple Card, the first credit card offering by Goldman Sachs, does not appear to be an isolated case, however.

Steve Wozniak, who invented the Apple-1 computer with Steven P. Jobs and was a founder of the tech giant, responded to Mr. Hansson’s tweet with a similar account.

“The same thing happened to us,” Mr. Wozniak wrote. “I got 10x the credit limit. We have no separate bank or credit card accounts or any separate assets. Hard to get to a human for a correction though. It’s big tech in 2019.”

In addition to Goldman Sachs, Apple partnered with Mastercard on the Apple Card, which the companies hailed as a revolutionary “digital first” credit card that had no numbers and could be added to the Wallet app on the iPhone and used with Apple Pay.