Downing Street's announcement of the meeting, which will take place on Tuesday, came after Jeremy Corbyn sent a letter to Boris Johnson calling on him to hold a Cobra meeting and "take personal charge" of the Government's response.
The Labour leader said he disagreed with the Prime Minister's assessment at the weekend that the flooding was "not looking like something we need to escalate to the level of a national emergency".
Mr Corbyn said that if the flooding had occurred in Surrey, rather than Yorkshire or the East Midlands, it would be "far more likely" that a national emergency would have been declared.
A Government spokesman said on Monday night: "The Prime Minister will chair an emergency COBR (Cabinet Office Briefing Rooms) meeting tomorrow to discuss the response to recent flooding."
In his letter to Mr Johnson, Mr Corbyn wrote: "With heavy rain expected in parts of Yorkshire and the Midlands, in areas that are already suffering from flooding, hundreds of further flood warnings are in place.
"Rightly there will be hundreds of thousands of people across these regions who remain concerned about their families and livelihoods.
"With this in mind, I am writing to urge you to hold a Cobra meeting and take personal charge of the Government's response to the devastating flooding we have seen over the past few days.
"In addition, we need full assurance from the Government that every resource is being utilised to aid those that need it and protect against future potential floods.
"With dozens of flood warnings still in place, I have to disagree with your assessment from the weekend that this is not a national emergency.
"If this had happened in Surrey, not Yorkshire or the East Midlands, it seems far more likely that a national emergency would have been declared.
"Every year we don't act means higher flood waters, more homes ruined and more lives at risk due to climate change."
Mr Corbyn said the Government must also ensure that the insurance industry fulfils its responsibilities.
On Monday afternoon, the Environment Agency had five severe "danger to life" flood warnings in place, all in and around Doncaster, as well as 39 flood warnings across the country.
Residents in Fishlake, near Doncaster, raised concerns that more flooding was likely from the River Don unless existing water was pumped away.
The Met Office has a yellow weather warning for rain in place until midday on Tuesday, covering parts of Stoke-on-Trent, Derby and Sheffield.
After the Cobra meeting was announced, a Labour spokesman said: "If these floods had happened in Surrey, this would have happened five days ago."