Goalkeeper Claudio Bravo, restored to the Premier League side’s starting line-up, did well by saving twice off Rajiv van La Parra and from Jack Payne’s free-kick in the first half, while Philip Billing had a goal ruled out for offside.
In front of a record crowd of 24,129, Terriers goalkeeper Joel Coleman kept out efforts from Nolito and Sergio Aguero in each half.
The draw for the quarter-finals takes place on Sunday at 18:30 GMT on the BBC News Channel, BBC Radio 5 live and the BBC Sport website.
Goalkeepers save the day
Both sides last met on this day in 2000 in the First Division with the game ending in a 1-1 draw, and it was a case of history repeating itself 17 years later.
City striker Aguero was given a first start in five matches, but the Argentine could not find a way past Coleman who was dominant in the air, keeping out the top-flight side with a total of four saves.
Coleman did make a rare mistake in the first half when he rushed off his line for the ball and was beaten to it by Aguero, but the City player’s lobbed effort failed to find the target.
City’s much-maligned goalkeeper Bravo, who had been dropped for the past four games, was in impressive form. He made three saves, the best of which came from Payne’s set piece which was heading for the top corner.
Can Town win the replay?
It will be a tough task at the Etihad Stadium and this may well have been a missed opportunity for the West Yorkshire side.
High-flying Huddersfield – third in the Championship – harried and hustled the opposition, allowing them no time on the ball and as a result, extended their unbeaten run to seven games in all competitions.
Top scorer Elias Kachunga [11 goals this season] and Nahki Wells [nine], were left on the bench and introduced only on the hour mark, but neither were able to trouble Bravo.
13 Coleman, 14 Craine, 5 Hudson, 27 Stankovic, 12 Holmes-Dennis, 4 Whitehead, 8 Billing, 18 Lolley Substituted forWellsat 59’minutes, 16 Payne Substituted forBrownat 72’minutes, 17 van La Parra Substituted forKachungaat 59’minutes, 23 Quaner
Manchester City :
1 Bravo, 5 Zabaleta, 24 Stones, 30 Otamendi, 11 Kolarov substituted forSagnaat 78’minutes, 25 Fernandinho, 6 Fernando, 18 Delph Substituted for De Bruyneat 69’minutes, 15 Jesús Navas, 10 Agüero, 9 Nolito Substituted for Sanéat 69′minutes.