Bangladesh are due to take on their hosts in the first Test beginning on Friday at Arnos Vale Ground in Kingston, before the second clash at Beausejour Stadium in St Lucia.
Left-arm spinner Sunny will take the place of Gazi, whose action was reported by umpires after the second one-day international with West Indies.
"I was very surprised at first," Sunny told Prothom Alo. "Let alone the national team, I wasn't even in the preliminary squad for Bangladesh A, though I was added later.
"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."