Howling winds and driving rain have disrupted transport links with travellers advised only to make journeys if absolutely necessary.
“Due to extreme and escalating weather conditions and in the interests of supporter and staff safety, today’s match has been postponed,” City said in a statement.
“This decision has been made by Manchester City’s Safety Officer following consultation with Club stakeholders and officials at West Ham United.”
The women’s Six Nations clash between Scotland and England was also postponed.
Saturday’s Calcutta Cup clash between Scotland and England’s men in Edinburgh had been marred by terrible conditions as England ran out 13-6 winners.
The only other Premier League game of the day is due to go ahead as Sheffield United host Bournemouth.