Nottingham Forest are enjoying a superb Premier League campaign, in third place with 57 points from 30 games, just four adrift of second-placed Arsenal.
Aina has been an influential figure for the club this term, but he has been ruled out for a number of weeks with a calf problem.
The 28-year-old, who has played all of the club's league matches this season, contributing two goals and an assist, picked up the knock in the 1-0 victory over Manchester United on Tuesday.
Espirito Santo said on BBC: "It is a problem with the calf. He [Aina] did the scan already, he's going to be out for a while. He will be unavailable [for the match against Aston Villa].
"It is a big one [losing Aina to injury at a crucial stage of the season]. His quality, his talent, the routines he already had [will be missed]."
Forest are next in action away to Aston Villa on Saturday.
Nottingham Forest manager Nuno Espirito Santo says he wants to add to the club's proud history as they prepare for their FA Cup semifinal clash against Manchester City at Wembley on Sunday.
Ahead of Tuesday night's Premier League showdown between Nottingham Forest and Manchester United, manager Nuno Espirito Santo has insisted that United remain a formidable opponent.
Nottingham Forest goalkeeper Matz Sels shone, denying Jack Taylor in a tense penalty shoot-out as the Reds beat Ipswich Town to reach the FA Cup quarter-finals.
Nottingham Forest have moved within striking distance of Premier League leaders Liverpool after a convincing 3-0 victory over Wolverhampton Wanderers.
