The US company also warned sales will fall for the first time later this year. It sold 74.8 million iPhones in its fiscal first quarter, compared with 74.5 million a year ago.
Apple said revenue for the next quarter would be between $50bn and $53bn, below the $58bn it reported for the same period a year ago.
This would mark Apple’s first fall in revenues since it launched the iPhone.
Despite first-quarter iPhone sales being below the 75 million expected by analysts, it was still a record quarter for the company.
Apple revenue in the three months to 26 December was $75.9bn and net profit was $18.4bn, both of which are the highest ever recorded by the company.
Sales of iPhones accounted for 68 per cent of the company’s revenue in the period.
Apple boss Tim Cook credited “all-time record sales of iPhone, Apple Watch and Apple TV” for the performance.
But the firm’s chief financial officer, Luca Maestri, said the company was operating in “a very difficult macroeconomic environment”.
He added that “iPhone units will decline in the quarter” and that the company was not projecting beyond those three months.
Maestri partly blamed the strong US dollar for Apple’s flat sales, estimating it had knocked $5bn off the company’s revenues
Apple’s sales in Greater China – defined by the company as China, Hong Kong and Taiwan – rose 14 per cent, but that was much slower than the 70 per cent increase a year ago.
Maestri said the softness in China was “something that we have not seen before”.
China accounts for almost a quarter of Apple’s sales, more than all of Europe combined.
The profitability of Apple’s business improved, with gross margin – or how much the company makes per product – increasing to 40.1 per cent.
Geoff Blaber, an analyst at CCS Insight, said Apple was “generating industry defying margins” and had cash of almost $216bn.
Speaking to analysts, Cook said the company had “the mother of all balance sheets” and that its financial position had never been stronger.
Apple’s shares were down 2.7 per cent in after hours trading at $97.28.
Daniel Ives, an analyst at Capital Markets who owns shares in Apple, said given the “white knuckles fears” ahead of the results, he would “characterise the overall headline performance as better than feared”, according to BBC.