"We would like to thank Steven for his hard work and commitment and wish him well for the future," a Villa spokesperson said in a statement.
Gerrard was appointed in November 2021 on a three-year contract but leaves following a poor start to the season that sees Villa only outside the Premier League relegation zone on goals scored after 11 games.
The former England captain endured chants of "getting sacked in the morning" by Fulham fans at Craven Cottage and Harrison Reed and Aleksandar Mitrovic scored for the home side on Thursday before a Tyrone Mings own goal completed Villa's misery.
"I thought I picked a team that could build on the performance [against Chelsea] at the weekend, but I got the opposite," Gerrard told Amazon Prime after the defeat.
"We were second best for the majority of the first half and were lucky to still be in the game at half-time, it was down to our keeper making some outstanding saves.
"The performance was nowhere near good enough.
"Tonight was a tough night for me personally. We will see what happens but I understand the situation we are in."
Gerrard replaced the popular Dean Smith last November after Villa's poor run, having been at Scottish club Rangers since 2018 and leading them to the title.
Villa's chief executive Christian Purslow spoke at the time of Gerrard taking the team to the next level, but the reality is the Midlands club are in worse shape than they were under Smith.
When Smith, who led Villa back to the top flight in 2019, was fired after five years in charge, Villa were 15th in the table with 10 points from 11 matches.
Under Gerrard this season they have nine from 11 and he led them to only 12 wins in 38 Premier League matches.
Villa have only scored seven goals and their struggles come despite Gerrard being backed in the transfer market with Philippe Coutinho, Lucas Digne, Diego Carlos, Boubacar Kamara and Leander Dendoncker all arriving.
Villa's next game is at home to Brentford on Sunday.
Information from Reuters was used in this report.