It is the first time Peterborough have reached round five of the competition since 1986. They also did so in 1981, losing 1-0 at home to City, the only previous FA Cup meeting between the two sides.
The price range for season ticket holders has also been reduced from £22-£32 to £18-£28.
The most expensive ticket for adults for league fixtures at the Weston Homes Stadium is £28.
The club said: “As the lowest ranked league club playing a home fixture in the fifth round of the Emirates FA Cup, we strived to strike a balance between revenue generation to allow for investment into the infrastructure of the football club following two years of revenue disruption due to Covid-19, but not to the detriment of our loyal fan base.
“We appreciate that initial balance was wrong and have amended the ticket prices.”