Adverse weather conditions in the north of England have made City's game unplayable and "unsafe" for matchday staff and fans, while building damage called off Everton's match.
Local police confirmed the news an hour before kickoff with strong winds making the game unplayable and "unsafe" for matchday staff and fans.
Minutes later, Everton announced that its match against Crystal Palace had also been called off.
A tweet from the Toffees official account said: "BREAKING NEWS: Tonight's game has been called off due building damage which has led to safety concerns."
A second tweet added: "Tonight's game has been postponed on police advice because of damage to buildings on Goodison Road."
City captain Kompany added on Twitter: "Game's called off! Make sure you get yourselves home and be safe, weather is terrible!"
An official statement from City said: "Manchester City can confirm that this evening's fixture versus Sunderland has been postponed due to exceptional and escalating weather conditions.
"The safety of those in around and travelling to the stadium complex cannot be guaranteed. This decision has been made by the Safety Officer and Greater Manchester Police.
"Both managers and the match officials understand and support this decision."
Weather conditions has also forced the Premier League clash between Stoke City and Swansea City to be pushed back to a 3:00 p.m. ET kickoff following a pitch inspection.