Mr Swinney said: "We are approaching a critical stage in the Falkirk West by-election campaign and it would be entirely inappropriate for New Labour to be awarded an unfair amount of broadcasting time.
They believe it will give Labour an unfair advantage in the run-up to the poll on Thursday, 21 December.
The election was called after sitting independent MP Dennis Canavan resigned from the seat.
The Scottish National Party Leader John Swinney described the timing of Tuesday's broadcast as "insensitive" and has suggested it should be excluded from the schedules north of the Border.
Mr Swinney said: "We are approaching a critical stage in the Falkirk West by-election campaign and it would be entirely inappropriate for New Labour to be awarded an unfair amount of broadcasting time.
"Falkirk West is a clear two-horse race between Labour and the SNP and we are urging the ITC as a matter of urgency to intervene by ensuring that this programme is either rescheduled until after the by-election or not screened in Scotland.
"Such insensitivity towards Scotland is yet another illustration of why broadcasting regulations should be devolved to Scottish institutions."
The Conservative Party Chairman, Michael Ancram, has written to the Independent Television Commission complaining the prime time slot is "unfair".
'Deep concern'
He said: "It beggars belief that this programme is not intended as a series.
"We are deeply concerned at the nature, timing and inherent unfairness of this programme."
The Tories have drafted in solicitors Clifford Chance to see whether ITV can be forced to screen other shows to avoid bias.
And the Liberal Democrats have also made a formal complaint.
A party spokesman said: "I am amazed at the naivete of ITV.
"No one can seriously believe Tony Blair can be on prime time television for an hour and not make a party political point, particularly this close to an election."
But London Weekend Television which is producing the show - to be hosted by broadcaster Jonathan Dimbleby - said Mr Blair was being given the opportunity in his role as prime minister, and not as a party leader.
And David Liddiment, ITV's director of programmes, defended the decision.
"This is a real chance for the voters to come head-to-head with the prime minister. We'll be putting to him the questions that are uppermost in the public's mind," he said.
Falkirk West by-election candidates
Iain Hunter, Scottish Socialist Party
Eric Joyce, Scottish Labour Party
David Kerr, Scottish National Party
Hugh O'Donnell, Scottish Liberal Democrat Party
Craig Stevenson, Scottish Conservative and Unionist Party
General election result, May 1997
Canavan, Labour: 22,772 (60.01%)
Alexander, SNP: 8,989 (23.4%)
Buchanan, Con: 4,639 (12.1%)
Houston, Lib Dem: 1,970 (5.1%)
Lab Majority: 13,783 (35.92% of the vote)
Electorate: 52,850
Total vote: 38,370
4% Swing from SNP to Lab