The striker, 29, apologised for his "actions in recent weeks" after he was pictured apparently partying immediately after their relegation from the Premier League earlier this month.
His subsequent suspension will be lifted by the club on Monday.
Agbonlahor said he "did not deserve" the captaincy.
"This role was a huge honour to me and it hurts to have lost it," added the striker, who has been "reminded of his responsibilities" by Villa.
He had previously been investigated in March, with Villa opting to take no further action, after being pictured on holiday in Dubai appearing to hold a shisha pipe.
"My celebrations and passion, especially in games against local rivals, shows my loyalty to Aston Villa," added Agbonlahor, who has spent 16 years at the club, in a post on Instagram.
"I am asking Aston Villa fans for forgiveness as I'm hurting as well despite reports and photos in the press making out otherwise.
"I agree my performances this season have not been good enough but I will be working hard to make things right! Up The Villa, Villa Till I Die!"
Agbonlahor - who had been put on a personal fitness plan before his ban - will miss Sat
urday's Premier League trip to Watford.
Source: BBC Sport