The 29-year-old was dropped for the 4-0 defeat by Chelsea on April 2 after pictures emerged of him apparently smoking a shisha pipe, but an investigation by the Premier League's bottom club resulted in no further punishment.
The striker, who has only scored once this season, also missed Saturday's 2-1 defeat by Bournemouth with a virus, and Black said he and Agbonlahor had agreed that action was required.
"We have decided together that we don't think he's up to the fitness levels of the Premier League at this moment in time," Black was quoted as saying by the club's website.
"He's got an individual programme that he will follow.
"Some of it will involve being with the group, some of it not with the group. We will reassess it in two weeks."
Villa, who play fifth-placed Manchester United at Old Trafford on Saturday, will be relegated if fourth-from-bottom Norwich City avoid defeat by Sunderland in the day's early kick-off.