A criminal investigation looking into the leaking of secret discussions of the National Security Council (NSC) could take place.
A Cabinet minister told MPs an official inquiry has not been ruled out.
The NSC, chaired by the Prime Minister, reportedly agreed on Tuesday to allow the tech firm access to build "non-core" infrastructure such as antennas, according to the Daily Telegraph.
This decision has been made despite some ministers allegedly voicing their opposition, including Jeremy Hunt, Sajid Javid, Gavin Williamson and Penny Mordaunt.
Their concerns are thought to be about the potential threat to national security.
Mrs May signalled her anger at the unprecedented breach in the secrecy.
Her official spokesman declined to say whether a leak inquiry had been launched, but told reporters: “The Prime Minister is clear that the protection of information on matters of national security is of the highest importance.”
And Culture Secretary Jeremy Wright told the House of Commons: “We cannot exclude the possibility of a criminal investigation.”
In a question to the House of Commons, shadow Cabinet Office minister Jo Platt said: “If a minister did leak the information, they are not fit to serve in the Cabinet – and are certainly not fit to be prime minister.
“Indeed, if the leak was for an advantage in a Tory leadership race that would be truly shocking.
“Critical issues of national security should be handled with utmost care, not used as political ammunition in a Tory party civil war.
“A full leak inquiry should be undertaken and, if identified, the individual should immediately resign or be removed from their position.”
Calls for a inquiry were backed by former national security adviser Lord Ricketts, who told the BBC it was the first major leak from the NSC since its inception in 2010.
He suggested investigators from the Security Service, MI5, could be brought in “to make the culprit feel very uncomfortable”.
Dominic Grieve, the chairman of the Parliamentary Intelligence and Security Committee, said the leak was “deeply worrying”.
“The principle that what is discussed at the NSC is kept totally confidential is really important,” he told the BBC.
“If it turned out that it was a member of the Cabinet – or indeed a minster who was attending the NSC – they should be sacked immediately.”
It is not yet clear on whether the leak is true and whether Huawei will be allowed to bid for contracts in the hi-tech communications project.
Mr Wright repeated the Government’s position that no final decision has been made yet.
The US has barred Huawei from involvement in official networks and put pressure on others to do the same over security concerns surrounding the company’s links with the Chinese government.