Sunny was due to leave Dhaka on Tuesday to join the team in St Vincent for the first Test, which starts on Friday.
Sunny, who has played four tests, will be the second specialist spinner in the squad along with uncapped left-armer Taijul Islam.
“I was very surprised at first. Let alone the national team, I wasn’t even in the preliminary squad for Bangladesh A, though I was added later,” said Sunny, who took 6 for 94 against West Indies in 2011, the best figures by a Bangladesh spinner on Test debut which has since been broken.
“I felt I had just fallen from the sky when some journalists called me on Friday evening telling me that I might be in the Test squad. I think I have recovered from the shock. I am feeling quite happy now”.
Sunny replaces Gazi who was reported by the umpires after the second ODI against West Indies.
He is required to be at the Cardiff Metropolitan University in the United Kingdom by September 19 to have his bowling action tested.