I don't believe Apple has a recommendation for a specific size in pixels, but their Human Interface Guidelines includes a section on labels that essentially just says they need to be legible:
You can use a label to name or describe parts of your UI or to provide short messages to the user. A label is best suited to display a relatively small amount of text.
Take care to make your labels legible. Don’t sacrifice clarity for fancy fonts or showy colors.
If you're looking for some more general indicators of size, you may want to look at their Icon and Image Creation Guidelines, which include many recommendations for the sizing of particular types of images and icons. For example, the following guidelines for icon size may give you some sense of how large to make your text if you want it to look reasonable in comparison with them.
For toolbar and navigation bar icons on iPhone, iPod touch, and iPad, create an icon in the following sizes:
About 20 x 20 pixels
About 40 x 40 pixels (high resolution)
For tab bar icons on iPhone, iPod touch, and iPad, create an icon in the following sizes:
About 30 x 30 pixels
About 60 x 60 pixels (high resolution)