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.
Nigeria international 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.