Trudeau told a briefing that 500,000 N95 surgical masks from Saint Paul, Minnesota-based 3M Co - part of a batch of 4 million ordered by the province of Ontario - should arrive on Wednesday.
Canadian officials pressed their US counterparts after Ontario complained the shipment had been blocked. US President Donald Trump signed an order last week to stop personal protective equipment from being exported.
"We have had constructive and productive conversations that have assured that this particular shipment comes through but we recognize there is still more work to do," Trudeau said.
"We are going to continue to highlight to the American administration the point to which healthcare supplies and services go back and forth across that border," he added.
The Canadian death toll rose to 345 from 293 on Monday, officials said. The total number of cases was 17,063, compared with 15,822 a day earlier.
The coronavirus outbreak looks set to cripple the economy, especially in the western province of Alberta, which was already suffering from low oil prices before authorities ordered a shutdown.
Alberta Premier Jason Kenney said on Tuesday that unemployment could increase to 25% from the current 7.2%.
"That's before we even fully account for the impacts of the crash in energy prices," he told reporters. "This will be the most challenging period in our economy, in relative terms, since the Great Depression."
The province's energy patch could need up to C$30 billion ($21.4 billion) in liquidity, he added. The federal government says it is working on an aid package for the sector.
Ottawa says more than 3.7 million people have filed unemployment claims since March 16, including for an emergency benefit that launched on Monday. Canada's workforce is around 20 million people, according to Statistics Canada.