The Labour leader stepped in as he asked what had happened to Mrs May and why she was not debating on the show.
Ms Rudd appeared on the stage in Cambridge alongside Labour leader Jeremy Corbyn, Liberal Democrat leader Tim Farron, Ukip's Paul Nuttall, Green Party co-leader Caroline Lucas, Leanne Wood of Plaid Cymru and Scottish National Party depute leader Angus Robertson.
Up to 3.3 million viewers tuned in to watch "May v Corbyn Live: The Battle for Number 10" on Sky News and Channel 4 on Monday evening, where the leaders were interviewed separately by veteran broadcaster Jeremy Paxman and a studio audience.
With May deciding not to take part, the Conservatives' home secretary Amber Rudd will represent her party at the televised debate in Cambridge instead.
Corbyn, the left-wing Labour Party leader, had initially meant to skip the debate himself, since the Conservative prime minister would not be present, but, buoyed by new polling that shows his party closing on the Conservatives and an assured performance in a televised forum earlier in the week, he changed course and tried to goad May into joining him.
"Support for Labour among younger voters has gone up and gone up dramatically but then the crucial question is whether these young people will come out to vote", Curtice said.
"The Tories have been conducting a stage-managed arm's length campaign and have treated the public with contempt".
He said: "Where do you think Theresa May is tonight?"
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Mrs May denied she was "frightened" of taking on her rivals head-to-head.
But Rudd got a different response, after the chair of the debate Mishal Husain reminded her that her party's manifesto had no costings.
"I've not been off the television screens, I've been doing things on the television, but predominantly taking questions from voters and listening to voters".
"Debates where politicians are squabbling among themselves doesn't do anything for the process of electioneering".
Another said: "Shocked to read that Amber Rudd's father died 48hr ago.even more fair play to her for tonight".
"Theresa May is not here but I hope to make a good fist of setting out Conservative Party policy".
Ms Rudd repeatedly accused Mr Corbyn of having a "magic money tree" - most notably after he attacked a Tory U-turn on disability benefits and accused the party of planning more cuts.
"Every single pollster, using whatever method, has found a rise in Labour support and something of a decline in Conservative support", said polling expert John Curtice.
Mr Corbyn was forced to defend his speech last Friday linking United Kingdom foreign policy to terrorism at home, claiming British military intervention in countries such as Libya had left "ungoverned spaces" which the extremists had been able to exploit to mount attacks.
The YouGov poll for The Times predicted the Tories would win 310 seats, down from the 330 they had when prime minister Theresa May called a snap general election, and short of the 326 needed for a majority.