The plans include the "real possibility" of calling on military assistance and preventing officers taking leave around the date of the UK's withdrawal in March 2019.
The document prepared by the National Police Co-ordination Centre (NPoCC) warns of traffic queues at ports with "unprecedented and overwhelming" disruption to the road network.
Home Secretary Sajid Javid told the BBC's Andrew Marr Show: "I'm glad the police and other experts are looking into this and thinking what might happen in a no-deal scenario."
He added: "I don't expect a no-deal outcome but we need to prepare for all contingencies."
Asked if the UK could face civil disorder resulting in widespread unrest, Mr Javid said: "I think it is right that Government prepares for all possible outcomes."
The leaked document obtained by the Sunday Times revealed concerns around medical supplies could "feed civil disorder", while a rise in the price of goods could also cause problems.
The potential for a restricted supply of goods raised concerns of "widespread protest which could then escalate into disorder".
It could also trigger a rise in non-Brexit related acquisitive crime such as theft.
The document, set to be considered by the National Police Chiefs' Council (NPCC) later this month, also sets out concerns about:
- EU police officers losing their legal right to carry a warrant card, potentially affecting 750 officers in the Metropolitan Police alone.
- Increased data costs hitting the budgets of forces which rely on mobile communication.
- Disruption potentially lasting for three months either side of the March 29 Brexit day, rather than the six weeks planned for by the Government.
- A perceived lack of communication between the Home Office and the Brexit department.
- The impact of the Operation Stack arrangements for queuing traffic at Channel ports being used at docks around the country.
Shadow police minister Louise Haigh lashed out at the Government's handling of the situation.
"This is the nightmare scenario long feared; according to the UK's most senior police officers, a no-deal Brexit would leave Britain on the brink," she said.
"But as the clock ticks, the Tories indulge in their own internal melodrama.
"Through their gross mismanagement, and their reckless flirtation with no-deal, the Tories are showing nothing but contempt for the safety and security of the British people.
"Years of Tory cuts have left the police overstretched and a no-deal Brexit would see our already grossly under-resourced police put under intolerable strain."
NPCC lead for operations Chief Constable Charlie Hall told the Sunday Times: "The police are planning for all scenarios that may require a police response in the event of a no-deal Brexit.
"At this stage, we have no intelligence to suggest there will be an increase in crime or disorder. However, we remain vigilant and will continue to assess any threats and develop plans accordingly."