Yes, it recited “Whereas the Provinces of Canada, Nova Scotia, and New Brunswick have expressed their Desire to be federally united into One Dominion under the Crown of the United Kingdom of Great Britain and Ireland, with a Constitution similar in Principle to that of the United Kingdom.”
This is a red herring occasionally, but rarely, raised. Most political scientists say this referred to responsible government, the parliamentary system as opposed to the American Presidential model.
Did it extend to the voting system?
1. Parliament has exclusive power
First, by section 44 of the 1982 Constitution Act, Parliament may exclusively make laws amending the Constitution of Canada in relation to the House of Commons. Provincial consent is not required. In 1867 we did not yet even use the secret ballot. Canada has made many changes to our voting system since then.
If winner-take-all single district elections were somehow entrenched in the constitution, they would equally be entrenched for provincial parliaments. But, similarly, section 45 of the 1982 Constitution Act says the legislature of each province may exclusively make laws amending the constitution of the province. That’s why Quebec's Charest government, in 2004, found no problem proposing a PR model similar to that introduced for Scotland's parliament -- in fact they pointed to that as a reason for it being acceptable for Quebec. That’s why BC, PEI and Ontario could legally vote on changing their voting system. That's why Winnipeg, Calgary and Edmonton were able to use the Irish STV system with multi-member districts for provincial elections from 1920 or 1926 to 1955 or 1958.
2. The UK was not wedded to winner-take-all elections in single member districts
Second, it’s a fallacy that the UK, in 1867, had nothing but single-member districts. In 1832 by the Great Reform Act about 62 ridings were represented by two MPs. Seven counties were now to have three MPs each instead of two. London had four MPs.
By 1867, four UK cities had three MPs each instead of two, but voters could only vote for two candidates. In London they could vote for only three of the four. This "limited vote" was an early attempt at a semi-proportional system. In 1868, for example, London elected three Liberals and one Conservative, while in 1874 it was three Conservatives and one Liberal. Also, in many two-member counties and boroughs the two main parties agreed to nominate one candidate each.
This all continued until 1885 when a new Reform Act provided that the majority of MPs would be elected in single-member constituencies. Canada had a number of two-MP ridings in 1867. And in 1885 Ontario copied the UK's "limited vote" in a Toronto riding with three MPPs, where voters voted for two, giving the minority one MPP, a model they kept for two elections.
The UK adopted proportional representation for Northern Ireland in 1920, and more recently for Scotland and Wales. Nothing unparliamentary about it
3. It’s only a preamble
Third, the Supreme Court of Canada,  1 S.C.R. 753, said "What, then, is to be drawn from the preamble as a matter of law? A preamble, needless to say, has no enacting force but, certainly, it can be called in aid to illuminate provisions of the statute in which it appears. Federal union "with a Constitution similar in Principle to that of the United Kingdom" may well embrace responsible government and some common law aspects of the United Kingdom's unitary constitutionalism, such as the rule of law and Crown prerogatives and immunities."
This is the common interpretation. Peter Hogg (Constitutional Law of Canada, looseleaf (Toronto: Carswell, 1992) at 9-3) has referred to Canada's system of parliamentary government, sometimes called responsible government, as "probably the most important non-federal characteristic of the Canadian Constitution." In responsible government, the executive is responsible to the legislature for its actions. But even if an executive that is responsible to the legislature is part of the Constitution, this does not mean that the way in which individuals are elected to the legislature is also part of the Constitution.
As the federal government argues in the current Supreme Court reference on the Senate "Thus, for example, although the preamble to the Constitution Act, 1867 refers to a “Constitution similar in Principle to that of the United Kingdom,” there is no compelling reason to read that clause as demanding an inquiry into what the 1867 framers thought that term meant in respect of the Senate, and then treating any deviation from the 1867 vision as requiring a more exacting amending procedure. In 1867, Sir John A. Macdonald foresaw an Upper Chamber of prosperous gentlemen of substance in the Upper House; he did not want an Upper House of landed nobility as found in Great Britain. But neither vision accords with contemporary expectations of who should sit in the Senate. The British themselves have repeatedly reformed their upper house to reflect modern democratic ideals."
4. It’s not arguable
Fourth, many books have been published on the pros and cons of proportional representation. For example, Prof. Dennis Pilon (“The Politics of Voting,” p. 76) shows the untruth of this claim. If an academically sound, or legally sound, argument on this point existed, I think I would have read it. But to the contrary, the Law Commission of Canada, in its 2004 Report, did not even find it necessary to discuss this argument. They stated "This Report aims to add corrective features to our electoral rules that do not involve constitutional amendments, and hence do not deal with Senate reform." These are top legal scholars. They would not overlook an arguable point.