“Due to the very difficult situation for the club, the team, my family and myself, I have decided to resign as coach of Werder Bremen with immediate effect,” Anfang said in a statement.
The 47-year-old has been at the centre of a scandal since Thursday, when it emerged he is under police investigation for using fake documents to claim he was fully vaccinated against Covid-19.
Anfang previously denied the allegations in a statement, which disappeared from the Bremen website by Saturday.
Managing director Frank Baumann told Bremen’s TV channel that there have been “further developments and a different state of affairs – the facts have changed”.
Assistant coach Florian Junge, who is also under investigation, has resigned alongside Anfang. Danijel Zenkovic, Anfang’s other assistant coach, is in charge for this evening’s match against Schalke, who were relegated alongside Bremen last season.
Both Schalke and Bremen are in mid-table as they bid to return to the Bundesliga.