Culture Secretary Nicky Morgan confirmed the decision, as part of the Telecoms Supply Chain Review, would now be made after the General Election on December 12.
The Chinese company has come under scrutiny over allegations of close ties to the Chinese state, with some critics arguing that its telecoms equipment could be used to spy on people in the West.
Huawei has always denied the allegations against it, insisting it abides by the laws of each country in which it is present.
Responding to a letter on the issue from the chair of the Foreign Affairs Committee, Tom Tugendhat, Ms Morgan said: “While it was this Government’s intention to conclude this aspect of the Review in the autumn, the General Election timetable and pre-election period mean that this will not now be possible.
“The decision will, therefore, be for the next government. I would expect that a future government would wish to inform Parliament of its decision, once made, at the appropriate time.”
The 5G decision had already been delayed from July after the Government said it was not in a position to make a final decision because of uncertainty created by the US government placing trade restrictions on the firm over security fears.
Major network operators have already begun rolling out their 5G networks across parts of the UK.
Foreign Affairs Committee chairman Mr Tugendhat said: “The Foreign Affairs Committee has been investigating the way the autocratic states intervene in democracies.
“Many members have been concerned about the Chinese technological dominance, nowhere more than in the 5G market. I wrote to the DCMS secretary to ensure that no decision would be made in the tail end of the government.
“I’m pleased to hear that a decision that could nest a hostile state’s technology deep in the central nervous system of the UK communications network will be taken by a new administration after a full debate.
“This decision has major foreign policy implications as it calls into question our most important security partnership, the Five-Eyes Alliance, and our economic relationship with other nations around the world, including Australia, Canada and the United States.”