Ferries between Dover and Calais and traffic using the Channel Tunnel could be disrupted until the end of September 2019.
A letter sent by Health Secretary Matt Hancock to the pharmaceutical industry and NHS contained the warning.
He said: “Although we cannot know exactly what each member state will do with respect to checks on the EU border, the cross-government planning assumptions have been revised so we can prepare for the potential impacts that the imposition of third country controls by member states could have.
“These impacts are likely to be felt mostly on the short straits crossings into Dover and Folkestone, where the frequent and closed loop nature of these mean that both exports and imports would be affected.
“The revised cross-government planning assumptions show that there will be significantly reduced access across the short straits, for up to six months.
“This is very much a worst-case scenario; however, as a responsible government, we have a duty to plan for all scenarios. “
Ministers are drawing up plans to fly in vital drugs and give priority to lorries carrying medical supplies at gridlocked ports.
Kent Council’s leader Paul Carter called for emergency measures to prevent lorries entering the county to avoid chaos on the roads.
“We now need far more input and information from national government in how they are going to work with us,” he said.
“There must be a national freight transport plan which, when necessary, can hold lorries back from coming into Kent in the first place should the need arise.”
The Border Delivery Group, a Whitehall co-ordination group for government departments that have an interest in border issues, was holding discussions with key stakeholders on Friday, a spokesman for Mrs May said.
The discussions centre on “the government’s no deal planning assumptions for the border”, the spokesman said.
Labour leader Jeremy Corbyn said “all options” – including a second referendum – must be on the table if Mrs May’s deal is rejected next week.
Writing in a national daily newspaper, Mr Corbyn made clear that his preferred result remains a general election.