There is no punishment for apostasy in Islam. In fact the Holy Quran stresses kindness and tolerance in matters of faith, the perfect example being the verse of the Holy Quran:
There should be no compulsion in religion. (Ch.2: V.257)
Islam stresses the freedom of religion, for example in Chapter 109 of the Holy Qur’an it states,
For you your religion, and for me my religion.
Furthermore there is not a single example of any punishment for apostasy from the life of the Holy Prophet(sa).
The Holy Quran states very clearly, that those who leave the Islamic faith and apostatise will be dealt with only by God Himself:
Those who believe, then disbelieve, then again believe, then disbelieve and then increase in disbelief, Allah will never forgive them nor will He guide them to the way. (Ch.4: V.138)
Nowhere is any punishment prescribed in this life as religion is a personal matter between man and God. People are therefore free to believe in any religion and to change their beliefs without any punishment from man. They will, however, be accountable for their beliefs before God.