World number seven Zvonareva said she has had inflammation in her right shoulder since last month's Kremlin Cup.
"She can't serve properly, therefore she has little chance against any of the Czech girls," Russia captain Shamil Tarpishchev told Reuters during Friday's draw at the Olympic indoor arena.
"I don't think we can be considered the favourites now," Tarpishchev said after being asked to assess his team's chances of winning their fifth Fed Cup title since 2004.
Zvonareva's place was taken by 27th-ranked Maria Kirilenko, who will face in-form Petra Kvitova in the opening rubber while Svetlana Kuznetsova will take on Czech number two Lucie Safarova in the second singles on Saturday. The two reverse singles will be played on Sunday followed by the doubles rubber.
Zvonareva's pull out did not surprise the Czechs.
"We knew she was not 100 percent fit so we weren't too surprised," said Czech captain Petr Pala. "But in any case, the Russian team is very strong and they have a lot of good players so it doesn't make our job any easier."
The Czechs, bidding for their first Fed Cup title since splitting from Slovakia in 1993, are led by Wimbledon champion Kvitova.
"I think it's still an open tie with a 50-50 chance for either team," said the tall left-hander, who has won two titles including last week's WTA Championships, in less than a month.
"It's the end of the season so everyone feels a bit tired by now. I'm a team leader and that puts extra pressure on me but I'm confident that I'll be able to play my best tennis here."