Reeves will deliver her first Budget on Wednesday in the Commons.
Last Friday, she outlined her plan to “change the way that we we measure debt” during a meeting of the International Monetary Fund (IMF) in Washington.
She explained she planned a technical change to loosen self-imposed limits on borrowing, to free up billions of pounds extra for infrastructure spending on projects such as roads, railways and hospitals.
The government has promised to get debt falling as share of the economy during the course of this parliament, rather than over a rolling five-year period.
Speaking in the Commons on Monday, Sir Lindsay said the policy changes “could hardly be described as a leak” when she had given on-the-record interviews, including to the BBC.
He said: “Ministers should expect to face proper, sustained scrutiny when these announcements are made to the elected members of this House and not the American news channels.”
This was because Reeves’ comments were major new policy announcements with “significant and wide-ranging implications for the government’s fiscal policy and for the public finances”, he added.
The Speaker said this was “totally unacceptable” and asked why Reeves expected MPs to wait “almost a week” simply to hear her repeat her announcements in her Budget statement.
MPs might be wondering, he added, “how they will get a seat on Wednesday. Well, to be honest the way it’s going you won’t need to – we’ll have all heard it.”
With Treasury minister Darren Jones making a statement to the House on “fiscal rules” later on Monday, the Speaker remarked: “Perhaps no coincidence.”
Alluding to previous breaches of parliamentary rules, Sir Lindsay noted that, when in opposition, Labour would complain about the previous Conservative government behaving in a similar manner, and demanded: “Get your acts together, all sides, treat Members with respect.”