Smith, 50, leaves following Villa's 1-0 defeat by Southampton on Friday, the club's fifth successive defeat in the Premier League.
Villa are 15th in the league, two points above the relegation zone.
"This year we have not seen the continuous improvement in results, performances, and league position which we have all been looking for," said Villa chief Christian Purslow.
He added: "For this reason, we have decided to make a change now to allow time for a new head coach to make an impact."
Villa says the process to replace Smith has started but they will not rush into an immediate appointment - however, it is understood that Denmark coach Kasper Hjulmand is a name of interest to the club and is admired by fellow countryman, Villa's Sporting Director Johan Lange.
Hjulmand guided Denmark to the Euro 2020 semi-final when they lost to England at Wembley, and the 49-year-old has a growing reputation.
Other names are also under consideration, with Villa using the time afforded to them by the international break to home in on Smith's successor.
Smith becomes fifth Premier League manager to lose a job
Smith was appointed Villa manager in October 2018, guiding them to promotion from the Championship in his first season in charge.
Though they struggled in their first season in the top-flight, narrowly avoiding relegation, Smith led the club to the 2019-20 Carabao Cup final.
The 2020-21 season saw Villa achieve an 11th place finish in the Premier League, but after the departure of star player Jack Grealish to Manchester City in the summer, results started to slip.
The club has not won since they defeated Manchester United on 25 September, picking up just 10 points from the first 11 games of the season.
It is their worst losing run since January to February 2017 in the Championship.
Smith leaves the club having won 28 of his 87 Premier League games in charge (32.2%) and with an overall win rate of 39.6% from his 139 games.
Smith is the fifth managerial change in the top flight this season with Tottenham sacking Nuno Espirito Santo on Monday and Norwich dismissing Daniel Farke late on Saturday.
