The party leadership is throwing its weight behind growing opposition to the sell-off.
Royal Mail managers this week voted strongly against privatisation, while the Communication Workers Union is threatening to ballot its members for a strike unless there is a deal on pay, pensions, jobs and other issues linked to the sell-off.
Labour MPs will stress the public and businesses rely on a daily delivery service and will warn that places where it is expensive or complicated to deliver the post every day - such as rural areas or blocks of flats - could be "vulnerable" if privatisation goes ahead.
The party is also warning many customers might have to travel miles to pick up large parcels. It says a privatised Royal Mail could choose to sell off its assets, such as local delivery offices.
A Labour source said: "In rural areas the local post office acts as a focal point for communities. There are also the small businesses that use the Royal Mail for ensuring customers get their goods and services on time and at a reasonable price.
"Which is why the Government's plans for privatising Royal Mail are so dangerous."
A Department For Business spokesman said: "This cynical scaremongering will not succeed in stopping our plans to ensure Royal Mail can thrive and deliver a better service to consumers and business.
"Regardless of ownership, Royal Mail will still be the UK's designated universal service provider and will continue to provide deliveries to all UK addresses - rural and urban - six days a week, only Parliament can change this.
"The Post Office is not for sale and there will be no programme of closures under this Government."