The German has left the Barclays Premier League strugglers by mutual consent less than a year after joining.
Almstadt and director of scouting and recruitment Paddy Riley have come under fire from fans for their roles in Villa's failed transfer business last summer, with the club bottom of the league.
A club statement read: "Aston Villa Football Club can confirm that sporting director, Hendrik Almstadt, has left the club by mutual consent with immediate effect.
"As part of the board's continuing assessment of (the set-up at the) Bodymoor Heath (training ground) it intends to conduct a thorough recruitment process to find a replacement."
The 40-year-old became the club's first sporting director when he joined from Arsenal, where he worked with Villa chief executive Tom Fox, last July.
Chairman Steve Hollis, who was appointed in January, has been conducting an internal review at the club with Villa set to be relegated from the top flight for the first time since 1987
Former Football Association chairman David Bernstein joined the board last week while ex-Villa manager Brian Little has been appointed as an advisor.
Lord Mervyn King, a former governor of the Bank of England, is also a new board member.
The club remains up for sale with owner Randy Lerner, who is based in the United States, stepping aside as chairman for Hollis at the start of the year.
Villa are nine points from safety in the Premier League, having won just three times this season, and go to Swansea on Saturday.
Source: PA