"I had already spoken with the club's bosses and we agreed it would be better if I step down," Silkin told reporters. "Yesterday's match showed the team needs a new direction."
Dmitry Khokhlov, Silkin's assistant last season, was named caretaker coach, Dynamo said in a brief statement on their website (www.fcdynamo.ru).
Former Russia international Khokhlov will make his debut against Dundee United in the Europa League second leg qualifier on Thursday. The first leg in Scotland ended in a 2-2 draw last week.
Silkin, 51, a long-serving Dynamo assistant coach who was promoted to the top job in April last year, became the first coaching casualty in the top flight three weeks into the season.
Sunday's defeat left Dynamo, founded in 1923 and the country's oldest football club, bottom of the league after losing their first three games. They have also failed to score a goal while conceding seven.
Last season, Silkin clashed with several leading players, including team captain Andriy Voronin, who accused the coach of lacking authority in the dressing room, although the team still managed to finish fourth in the league.
Former Ukraine and Liverpool striker Voronin last week accepted a one-year loan deal to join Bundesliga club Fortuna Duesseldorf.