The decision makes Lamouchi the first managerial casualty of the tournament.
According to journalist Romain Molina, the move was confirmed in the hours after the defeat, with Molina writing that Lamouchi's time in charge of the Carthage Eagles had come to an end.
Tunisian radio station Mosaique FM reported that federation officials called an emergency meeting to discuss Lamouchi's position immediately after the result.
There were also reports of fights breaking out within the Tunisia camp at full-time, and again later at the team hotel.
Lamouchi, who previously managed Nottingham Forest and Cardiff City in England, had been in charge of Tunisia for only five games since his appointment in January.
His side had gone through World Cup qualifying without conceding a goal, but were torn apart inside six minutes by Sweden, with Yasin Ayari and Alexander Isak both scoring in the opening half hour.
Omar Rekik pulled one back for Tunisia with his first international goal, but the second half belonged to Sweden.
Victor Gyokeres, Mattias Svanberg and a second Ayari goal completed the rout.
"It's a difficult loss. It's painful," Lamouchi said after the match.
"With world-class players that we have in the two Swedish forwards, it's something that you don't recover from. We made way too many mistakes."
Wahbi Khazri, the former Sunderland and Saint-Etienne forward who retired in December and joined Lamouchi's staff as head of analysis, is reported to be the leading candidate to take interim charge.
A 74-cap former Tunisia captain, Khazri would be tasked with steadying the squad ahead of their second Group F match against Japan.
Questions were also raised after the match about the presence of Lamouchi's son within the camp, with a witness telling Mosaique FM that a confrontation broke out between a supporter and the coach's son.
Lamouchi addressed the issue directly when asked by reporters.
"As a father I'll answer you first, and it's also the coach who'll answer you. I'm sure there are family connections here, but my son plays no part in the selection process."
He explained his son had travelled with extended family for Eid and was not part of the technical staff.
Tunisia now face a rapid turnaround, with their World Cup survival already looking precarious after one round of fixtures.
The Carthage Eagles' next assignment against Japan takes on far greater significance than anyone expected when the group stage draw was made.