According to Research Publications, Library of Parliament
3.2.3 What happens if a prime minister dies or is incapacitated while in office?
There are few procedural implications if the prime minister dies while in office. If it happens while the House of Commons is sitting, the House may adjourn for an extended period. Only two prime ministers have died in office: Sir John A. Macdonald on 6 June 1891 (during a session) and Sir John Sparrow David Thompson on 12 December 1894 (while Parliament was prorogued). Macdonald was succeeded by John Abbott, a senator, and Thompson was replaced by Mackenzie Bowell.
The incapacity of a prime minister would be more problematic; no precedents exist for this situation.https://lop.parl.ca/sites/PublicWebsite/default/en_CA/ResearchPublications/202128E#a21---
Justin Trudeau's father, Pierre Trudeau, created the position of Deputy Prime Minister in 1977, but as I understand it, there is no requirement for anyone to be appointed to that position.
So the short answer is, for the present government, the Deputy PM. That is Chrystia Freeland.
https://deputypm.canada.ca/enIf no deputy PM is appointed, the Privy Council would provide a list of succession. Being a member of the Privy Council is a lifetime appointment, but only Privy Councillors presently serving in cabinet can generate an OIC and make a list. From what I remember from school, the job goes to a line of senior ministers. That is, from the most to the least senior in the cabinet.
The longer, more complex explanation is the Governor General would appoint someone.
There is a list that Trudeau's government made that outlines the ministers who would be appointed should he become incapacitated or die.