Davis is one of three players missing from Michael O'Neill's squad that beat Greece 2-0 last month, with goalscorer Jamie Ward and Ryan McLaughlin also absent.
The Northern Ireland skipper's absence is due to a hamstring injury sustained in Southampton's victory over Leicester City last weekend and represents a big blow for O'Neill.
Ward netted the opening goal in victory over Greece last month and had been in impressive form for Derby County before being sidelined by a thigh strain almost a month ago.
Attacker Niall McGinn insists they can go to Bucharest with confidence, despite the missing players, and look to make it four wins from four.
"We're at a stage now where we are first in the group, and I think we're all confident lads and training has been going well and the games have been going well and we just want to stay there as long as possible," said McGinn.
"And hopefully on Friday night we can go out there and put in another good performance."
Anghel Iordanescu's Romania side are also unbeaten in the opening three matches but trail O'Neill's side by two points after a draw with Hungary last month.
"I will use the same system, 4-2-3-1, but I want the team to play offensively," he said. "The game against Northern Ireland is extremely important.
"I have studied our opponents, they are a team are dangerous at all times, especially from counter attacks and set pieces."
