Zinchenko was visibly moved by the displays of solidarity with his homeland, in the wake of Russia's invasion of the country, during City's Premier League game at Everton on Saturday.
The full-back was an unused substitute at Goodison Park but is poised to return to the field as City travel to the Championship strugglers in the fifth round.
Guardiola said Zinchenko was "absolutely fine" and in the right frame of mind to play: “I think it will be good for him to play and show the reason why he is here. He is a magnificent player (and) needs to play football."
Zinchenko attended an anti-war vigil in Manchester last week and on Monday added his voice to calls for Russia to be excluded from international sport. The 25-year-old shared a statement on Instagram calling on governing bodies to ban Russia and its athletes from international competitions and impose restrictions on the country concerning media and sponsorship.
City head to the Weston Homes Stadium after moving six points clear at the top of the Premier League with a controversial 1-0 success at Everton. Phil Foden's 82nd-minute effort proved decisive, and Guardiola’s side will be strong favourites to prevail against a Peterborough side languishing at the bottom of the Championship.
Posh have not won in the league for more than two months and last week parted company with manager Darren Ferguson, replacing him with Grant McCann.
Guardiola said: "It is one game, a final. Of course they are not in the best position in the Championship, but it is a game in a stadium with conditions that we will have to adapt to.
"We will prepare well to try to go through and get to the quarter-finals."
McCann said his side have nothing to fear, despite rubbing shoulders with some of football’s elite players.
"We're playing against one of the best teams in the world at the moment. So, all we can do is go and look forward to it, the boys are excited about it.
"The game’s on TV, it's going to show people what we are about, what you're about as footballers - there's nothing to be scared of, really.
"I take myself back to when I was playing. It's one of these games you think: 'Well, it's an opportunity to go and show everyone'.
"No one from the outside looking in will give us any sort of hope of winning the game. So the boys need to embrace it, go and play with a smile on their face and see what happens."
Meanwhile the Manchester City manager also discussed the departure of Marcelo Bielsa, a long-time role model for Guardiola, who left Leeds this week, replaced by Jesse Marsch.
"I'm so sorry for him," said Guardiola. "His legacy is there, in the Leeds city and club, and I'm pretty sure with the players. His influence is massive.
"Unfortunately all managers are subject to results, and maybe they were not good, but the games played in three or four seasons at Leeds were spectacular to watch and I wish him all he best in future."