Sweden inflicted the heavy loss on Tunisia in their Group F opener at the Estadio Monterrey in Guadalupe, Mexico, with Yasin Ayari, Viktor Gyokeres and Alexander Isak all finding the net.
Reports immediately after the match suggested Lamouchi had already been removed, but sources told the BBC the 54-year-old had taken training as normal on Monday before the federation's official confirmation followed shortly after.
"An agreement has been officially reached to dismiss coach Sabri Lamouchi," the federation said in a statement.
"Plans are under way to appoint Mondher Kebaier as the national team coach."
Lamouchi's sacking makes him the first manager in World Cup history to be dismissed after just a single match of the tournament.
The Frenchman had only been appointed in January, taking over from Sami Trabelsi, who left the role following a last-16 exit to Mali at the Africa Cup of Nations.
Lamouchi won just one of his five matches in charge of Tunisia, a 1-0 victory over Haiti in his first fixture at the helm.
The warning signs had been building before the World Cup. Tunisia lost 1-0 to Austria and were then beaten 5-0 by Belgium in their two warm-up fixtures earlier this month.
Speaking after the defeat to Sweden, Lamouchi did not hide his frustration with his players' performance.
"Starting the competition with this bad of a loss is indeed difficult," he said.
"We made too many mistakes, and this is not something that we can do. We are shooting ourselves in the foot, we are hurting ourselves."
Mondher Kebaier, who is expected to take interim charge for Tunisia's remaining group fixtures, previously managed the national team between 2019 and 2022.
During that spell he guided Tunisia to the final of the Arab Cup in 2021, losing to Algeria, before exiting at the quarter-final stage of the Africa Cup of Nations the following year.
Kebaier has more recently served as the federation's technical director, putting him in a position to step in at short notice as Tunisia look to salvage their World Cup campaign.
Lamouchi's removal continues a pattern of instability that has now produced two managerial changes for Tunisia within roughly six months, following Trabelsi's exit in January.
Tunisia face Japan in their second Group F fixture, before a final group match against the Netherlands.
With a four-goal deficit already on the board, the Carthage Eagles' path out of the group stage now looks considerably steeper than it did a week ago — and Kebaier inherits a squad that will need an immediate response just to keep their tournament alive.