Rabada returned to South Africa while playing in the ongoing Indian Premier League League (IPL) last month with his franchise, Gujarat Titans, saying he had to deal with an "important personal matter".
In statement issued by Rabada through the South African Cricketers' Association (SACA), the paceman said he is "deeply sorry" for his actions and is looking forward to playing again.
The statement said: "As has been reported, I recently returned to South Africa from participating in the IPL for personal reasons. This was due to my returning an adverse analytical finding for the use of a recreational drug.
"I am deeply sorry to all those that I have let down. I will never take the privilege of playing cricket for granted. This privilege is much larger than me. It goes beyond my personal aspirations.
"I am serving a provisional suspension and I am looking forward to returning to the game I love playing.
"I couldn't have gone through this alone. I'd like to thank my agent, CSA, and Gujarat Titans for their support. I'd also like to thank SACA and my legal team for their guidance and counsel. Most importantly I'd like to thank my friends and family for their understanding and love.
"Moving forward, this moment will not define me. I will keep doing what I have always done, continuously working hard and playing with passion and devotion to my craft."