The decision was prompted by the lack of public support for electoral reform, Democratic Institutions Minister Karina Gould said.
Repeating a pledge made throughout the 2015 campaign that brought the Liberal Party to power, Trudeau vowed in his government's first policy speech that that year's vote "will be the last federal election conducted under the first-past-the-post voting system."
Proposed alternatives had included a system of proportional representation and ranked ballots.
Opposition parties on both sides of the issue have accused the Trudeau government of faltering on its commitment and of seeking to push through big changes without holding a referendum.
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However, "major reforms to the electoral system, changes of this magnitude, should not be made if they lack the broad support of Canadians," she told a news conference.
Following public consultations, she said, "it has become evident that the broad support needed among Canadians for a change of this magnitude does not exist."
Results of an online survey of 380,000 respondents released last week found that 67 percent of Canadians are "somewhat or very satisfied" with the current system.
However, it showed that many also hold conflicting views -- wanting an "easy to understand" electoral system that also produces more collaborative parliaments.