Sadomba is the top scorer in this year’s African Champions League, having scored seven times so far.
But the Sudan-based forward picked up a shoulder injury during Al Hilal’s semi-final defeat to Esperance on Sunday.
The Warriors must beat Cape Verde if they are to have any chance of qualifying from Group A.
However, Zimbabwe were a day behind schedule and flew to Cape Verde, via South Africa, on Tuesday afternoon.
This means the squad will have just two full days to train in Praia ahead of the match, having chosen to break with tradition by having no training camp at home.
With one round of matches left, Mali top the table with nine points, one more than Zimbabwe and two more than Cape Verde.
Liberia, who host Mali on Saturday, bring up the rear with four points and are the only team in the group who cannot qualify.
Zimbabwe have not qualified for a Nations Cup since reaching the 2006 finals, which constituted only their second appearance ever. BBC