Former midfielder Freddie Ljungberg was appointed Arsenal's interim manager on Friday after Unai Emery was sacked as manager in the wake of a seventh game without a win.
The north Londoners lost their Europa League group stage game on Thursday night to continue the club's worst run since 1992.
Arsenal's players were booed off at the end of the 2-1 defeat to Eintracht Frankfurt at the Emirates Stadium.
The club directors responded by dismissing the man they brought in 18 months ago to replace Arsene Wenger who had led the team for two decades.
"The search for a new head coach is underway and we will make a further announcement when that process is complete," said a club statement.
Arsenal's fans had demanded decisive action from directors with the club's run of five draws and two defeats this season one match off equalling George Graham's sequence of eight without a win in 1992.
Ljungberg, 42, scored 72 goals in 318 appearances for Arsenal between 1998 and 2007. He was appointed assistant first team coach last June.
Among those mooted for the permanent job include the former Arsenal playmaker Mikel Arteta, who is Pep Guardiola's assistant at Manchester City, the ex-Juventus and AC Milan coach Massimiliano Allegri as well as the Wolverhampton Wanderers boss Nuno Espirito Santo.
Emery arrived at Arsenal in May 2018 after two seasons at Paris Saint-Germain where he won seven trophies including the 2018 French championship and two French cups.
At the end of his first season, Arsenal reached the final of the 2019 Europa League where they were thrashed by Chelsea 4-1.
His second season in London has been undermined by the poor performances of the players.
Emery had to strip Granit Xhaka of the captaincy after the Swiss international swore at Arsenal fans when he was substituted against Crystal Palace last month.
And Nicolas Pepe, the club's record signing, has failed to sparkle since his 84 million euro transfer from Lille.
"Our most sincere thanks go to Unai and his colleagues who were unrelenting in their efforts to get the club back to competing at the level we all expect and demand," said the club statement.
"We wish Unai and his team nothing but future success. The decision has been taken due to results and performances not being at the level required."