That replay is likely to be played in about 10 days' time, stuck-in between the Leicester City and Brighton games, a week before going back to the Emirates for the second leg of the League Cup semifinal.
Championship side Norwich rarely threatened themselves but will be more content with the result than Chelsea, who also face Arsenal in the two-legged semi-finals of the Carabao Cup over the next few weeks, live on Sky Sports.
Norwich came close to a famous victory in the first half when Alex Pritchard managed to intercept David Luiz's clearance, but he was unable to keep control of the ball. At the end I think Norwich deserve a replay at Stamford Bridge.
Chelsea have progressed from 20 of their last 21 FA Cup ties against non-Premier League sides, with the exception their 4-2 defeat to Bradford in January 2015.
The Brazilian saw a couple of shots saved by Gunn and also picked out Drinkwater with a low cross from which he fired wide.
Kenedy also featured, as did the returning David Luiz, in a much-changed line-up.
Chelsea were abysmal in the first half, but looked slightly brighter when they came out after the break. A draw is a totally fair result.
Conte admitted: "For sure there is a bit of disappointment because we have another match in a schedule that is so busy". We had an outstanding game and in the first half we dominated, and didn't give a chance away. When you play in this trophy you know it is very hard, but today the commitment of my players was very good.
While Willian tried to make something happen for Chelsea, he could not find a way past Norwich's defence, with Zimmermann particularly impressive in the back three.
"Don't forget that Michy is a young player".