The Taiwanese firm, also known as Foxconn Technology, posted a net profit of NT$37bn ($1.2bn; Â£814m) in the October to December quarter.
It also reported a 16% jump in full year profit for 2012 to NT$94.8bn.
Foxconn is the world's biggest contract electronics maker and Apple is one of its biggest clients.
According to some estimates, orders from Apple account for almost half of Foxconn's total revenue.
In the October to December quarter, Apple had sold 47.8 million iPhones, up from 37 million a year earlier.
Meanwhile, the launch of iPad mini, also boosted sales of its tablet PCs - it sold 22.9 million iPads, compared with 15.4 million in the same period in 2011.
However, the heavy reliance on Apple has also raised concerns that Foxconn's growth may slow in the coming months.
Some analysts said the rapid rate of growth that smartphones and tablet PCs had seen in recent years could not be sustained.
"In most of the developed economies, smartphones are at a mature penetration stage and tablets are pretty close to being at that stage," said Andrew Milroy of consultancy firm Frost & Sullivan.
Mr Milroy added that Apple had so far not been able to replicate the success it enjoyed in the developed economies in emerging markets.
He explained that in the emerging economies, Apple products were still very expensive and out of reach for many consumers.
At the same time, Apple is facing increased competition from other smartphone makers in those markets.
"They are being hammered by low-cost smartphones in countries such as China," he said.
The fear is that if Apple's growth rate slows, it will have a knock on effect on suppliers such as Foxconn.

Southern Cross is holding a crisis meeting with landlords, lenders and government officials.
Of central importance is how to ensure continuity of care for the 31,000 people at the firm's 751 care homes.
The care home provider says it cannot afford to pay the full rent on its homes.
Families and staff 'in the dark'Q&A: Care home closures
Landlords will agree to a compromise in order to allow the care home provider to remain solvent, the BBC's business editor, Robert Peston, has learned.
The restructuring may leave the Darlington-based firm with just 250 to 400 homes, with the others being taken over by different care providers.
But the biggest landlord, NHP, which owns 249 of the homes, is expected to stick with Southern Cross.
The government has been putting intense pressure on landlords not to abandon Southern Cross altogether, according to Robert Peston.
Southern Cross said last month it planned to stop paying about a third of its rental bill.
The company's landlords met on Monday, and are expected to table their own proposal for the firm's future at the meeting on Wednesday.
"The landlords have agreed in principle that they will make significant financial concessions in order to achieve a sustainable solution," said Daniel Smith, who chaired their meeting on Monday.
By Robert PestonBusiness editor, BBC News
Read Robert Peston's blog
"Our overriding concern at this time remains minimising disruption and concern for residents and their families."
In return, it is expected that the government and lenders will also agree to write off some of the money Southern Cross owes them.
Under their joint proposal, individual landlords would reportedly be given various options, including:
Southern Cross is the UK's largest care home operator, employing 44,000 staff, of which the company has already said it will cut 3,000.
Hon Hai Precision Industry, a major assembler of Apple products, has posted record quarterly profits helped by growing demand for iPhones and iPads.
[NEXT_CONCEPT]
Landlords at troubled care home provider Southern Cross have pledged to do all they can to help it avoid bankruptcy, the BBC understands.