Villa are nine points adrift at the bottom of the Premier League having won just three games all campaign and could go down on Saturday.
"In the current circumstances, we are sure our supporters will understand," a club spokesman said.
There have been several fan protests against owner Randy Lerner, including during the recent home loss to Chelsea.
During the game, supporters held up banners that read: "Proud history, what future?"
Villa supporter Mike McKenna, who organised the recent fan walkout protests during home games against Everton, Tottenham and Chelsea, said: "There is a toxic atmosphere at the club at the moment. The players are not generally well liked.
"Unfortunately, the complaints about the likes of [Micah] Richards, [Gabriel] Agbonlahor, etc have rubbed off on other players.
"Maybe Jordan Ayew deserved an award but, with the toxic atmosphere, the club have thought it would only garner bad publicity to garnish the players with awards.
"Generally, I would think the supporters support the decision not to have awards as there is nothing to celebrate."
Villa have sacked two managers this season - Tim Sherwood in October and his successor, Remi Garde, last month.
Eric Black is in temporary charge and has overseen two successive defeats, the most recent of which came at home to Bournemouth on Saturday.
Villa's relegation will be confirmed if Norwich avoid a home loss by Sunderland in the 12:45 BST kick-off on Saturday.
Even if the Canaries lose, Villa still need to win against Manchester United at Old Trafford later in the day to avoid dropping out of the Premier League.
Aston Villa have cancelled this season's player of the year awards with the club facing relegation.