While Apple did not reveal the exact number of phones affected, The New York Times said that "its statement implied it was a few thousand phones". The New York Times also pointed out that "a manufacturing issue is not the same as a defective battery".
The New York Times - "We recently discovered a manufacturing issue affecting a very limited number of iPhone 5S devices that could cause the battery to take longer to charge or result in reduced battery life,” said Teresa Brewer, an Apple spokeswoman. “We are reaching out to customers with affected phones and will provide them with a replacement phone.”
This isn't the first time Apple had battery problems on its devices. In December 2012, there were reports of iOS 6.0.2 causing battery to drain faster on the iPhone 5 and iPad mini. When Apple launched in the iPhone 4S in 2011, the device also had battery drain issues which it subsequently addressed via a software update.