Voronin is a former Ukraine international who featured 75 times for his country and played at the 2006 FIFA World Cup and 2012 European championships.
The 42-year-old has taken the decision following Russia’s invasion of Ukraine which has attracted worldwide criticism.
Voronin has since headed for Germany, where he once played for Borussia Monchengladbach, Mainz 05, FC Cologne, Bayer Leverkusen, Hertha Berlin and Fortuna Dusseldorf.
A statement from Dynamo Moscow read: "Football club 'Dynamo' and assistant head coach Voronin reached an agreement to terminate the contract by agreement of both parties."
"I could no longer work in the country that is bombing my homeland," Voronin told Bild.
"We got out of Moscow before it was completely blocked."
"We couldn't land in Dusseldorf so we flew via Amsterdam. My father, my mother-in-law, my wife and my children are here now.
"I've been unwell for four days. Really bad. When I see all the pictures from my homeland. When I see the news. It's all as unreal as a movie. But a horror film.
"I just want to help. With money. Whatever... And I don't know if I should say it: But if I were in Ukraine right now, I'd probably have a gun in my hand too."
