The Robins produced the shock of the tournament so far as they dispatched holders Manchester United 2-1 at Ashton Gate this week, with Korey Smith snatching the winner in the 93rd minute.
Bristol will now face another Manchester giant in City in the semi-finals after the Citizens saw off Leicester City in a penalty shoot-out on Tuesday.
The other semi-final will see Chelsea take on Arsenal after the Blues saw off Bournemouth 2-1, with Alvaro Morata scoring the winner in the 91st minute, around 60 seconds after Dan Gosling had temporarily equalised for the Cherries.
The semi-final ties will take place over two legs in the week commencing January 8.
Carabao Cup semi-final first-leg fixtures:
Chelsea v Arsenal
Manchester City v Bristol City