Edit: Version 1.5.0 (July 2017) of the Extensions to the PNG 1.2 Specification has finally added an EXIF chunk. It remains to be seen if encoders-decoders begin to support it.
Original: PNG does not embed EXIF info. It allows, however, to embed metadata "chunks" inside the image. Some of the standardized chunks correspond to a few EXIF attributes (physical dimensions, timestamp). And it's also possible to store arbitrary textual data as
key=>value pairs, or to define new chunk types. So, you could in theory store any EXIF information... but, alas, in your own custom format. Some attempts to standarize have not caught up, it seems.