Germany were left humiliated when South Korea scored two stoppage time goals in the final Group F game, consigning the reigning champions to bottom spot and an early flight home.
Loew has been in charge of Germany since 2006, reaching at least the semi-finals of every major tournament he took them to – until this year.
The charismatic 58-year-old had only extended his current Germany contract until the summer of 2022 earlier this year.
Loew has a record better than any other Germany manager in history, winning 108 of his 165 games in charge.
But poor performances heading into the World Cup saw fans jeering in stadiums during their warm-up games.
The fans’ concerns were justified when they suffered a 1-0 defeat to Mexico on the opening day of their tournament.
It took a 95th minute Toni Kroos strike to secure a victory over Sweden, but the surprise 2-0 loss to South Korea consigned Germany to their most miserable day.