Anfang, who on Friday denied using a fake certificate, said he was resigning for the good of the club and the team. His assistant coach Florian Junge also stepped down.
"I decided to terminate my role as head coach at Werder with immediate effect given the burdensome situation for the club, the team, my family and me personally," Anfang said in a club statement.
Werder, playing in Germany's second division this season, had said on Friday an investigation was underway over the coach's vaccination certificate, with Anfang saying he had done nothing wrong and that he had been vaccinated twice at an official vaccination centre.
He said he had then digitised his vaccination certificate at a pharmacy.
"Markus and Florian show responsibility with this decision and contribute to ending the turmoil of the last days surrounding the team," said Werder managing director Frank Baumann.
"We respect this decision and will start the search for a new head coach."
The vaccination of players and team staff has been an issue for months in German football.
Bayern Munich midfielder Joshua Kimmich has triggered a heated public discussion as the most high-profile player to refuse inoculation and cited concerns over the long-term effects of the vaccine.
Formula One stewards handed Haas rookie driver Oliver Bearman a 10-place grid drop for his first home British Grand Prix for failing to comply with red warning flags in Saturday's final practice.
Seventh seed Mirra Andreeva outclassed American Hailey Baptiste 6-1 6-3 under the Court One roof to equal her best Wimbledon run by reaching the last 16 on Saturday.
Carrying a red floral wreath bearing his shirt number, Diogo Jota's Liverpool teammates joined relatives and residents in a small Portuguese town on Saturday for the funeral of the football star, who died with his brother in a car crash on Thursday.
An 83rd-minute Weverton own goal from a deflected Malo Gusto cross gave Chelsea a nervy 2-1 win over a spirited Palmeiras side in the Club World Cup quarter-finals on Friday.
Women's top seed Aryna Sabalenka fought off inspired home favourite Emma Raducanu in a cauldron-like Centre Court atmosphere to keep her Wimbledon quest on track but it was the end of the road for two other Grand Slam champions on Friday.