The Conservative leader will use Tuesday's regular cabinet meeting to "remind" colleagues to keep their discussions private and urge them to focus on the job of government, he said.
Ahead of the resumption of key Brexit negotiations in Brussels on Monday, the weekend newspapers were filled with stories about warring ministers, as well as leaks targeting Finance Minister Philip Hammond.
"Cabinet must be able to hold discussions on government policy in private and the prime minister will be reminding her colleagues of that at the cabinet meeting tomorrow," May's spokesman said.
Hammond hit back Sunday, blaming the "noise" on rivals who disagreed with his position that Britain must be careful to prioritise the economy when it withdraws from the European Union.
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But his words seemed only to fuel the fire, with an unnamed cabinet minister accusing him in Monday's Daily Telegraph of trying to "frustrate" Brexit.
"What's really going on is that the establishment, the Treasury, is trying to **** it up. They want to frustrate Brexit," the minister said.
The minister said Hammond viewed Brexit supporters as "a bunch of smarmy pirates" who have "taken the establishment prisoner".
The ruling Conservatives lost their parliamentary majority in the June 8 vote, greatly weakening May's authority, although she remains in office as the head of a minority government.
Since then, individual ministers have publicly given different views on how Brexit should proceed, while media reports suggest some are manoeuvering for a possible leadership contest.
Asked if the premier thought Hammond was trying to frustrate Brexit, May's spokesman said: "The government is all working together to deliver a Brexit which delivers on the will of the British people.
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