Levi won the award for equalling West Indian Chris Gayle's record highest score of 117 during the tour of New Zealand earlier this year.
In the process, he made the fastest Twenty20 International century of all time (off 45 balls) and also hit the most sixes ever in a T20 innings (13).
"It was a phenomenal performance and one that is going to be talked about for years to come," said CSA acting CEO Jacques Faul.
"To win the award he had to beat off serious competition from the likes of Gayle and Sri Lanka's Tillakaratne Dilshan.
"We congratulate him on his achievement and hope this augurs well for the ICC World Twenty20."
Levi was the only South African to be honoured with an ICC award this year.
Hashim Amla and Vernon Philander were both in the running for the 'Test Player of the Year' and 'Cricketer of the Year' but Kumar Sangakkara of Sri Lanka won both the trophies.