Labour's Jeremy Corbyn accused the PM of "dodging" a head-to-head showdown and the Lib Dems urged broadcasters to "empty chair" her.
Mrs May sprung a surprise by announcing she would seek a poll on 8 June rather than wait until 2020, promising "strong and stable leadership" if she wins.
MPs are expected to back the early election in a vote on Wednesday.
Live TV debates took place for the first time in a UK general election in 2010, and the experiment was repeated in 2015 using a range of different formats.
Asked about the snap general election, a Number 10 source said: "We won't be doing TV debates."
Mr Corbyn said the PM's stance was "rather strange", adding: "I say to Theresa May, who said this election was about leadership, Come on and show some.'
"Let's have the debates. It's what democracy needs and what the British people deserve."
Liberal Democrat leader Tim Farron added: "The prime minister's attempt to dodge scrutiny shows how she holds the public in contempt.
"The British people deserve to see their potential leaders talking about the future of our country."
A BBC spokesman said it was too early to say whether the broadcaster would put in a bid to stage a debate.
Drawn-out negotiations were needed between the political parties and broadcasters before the 2015 debates could take place.
They included a seven-way party leaders' TV debate, which was watched on ITV by an average audience of 7 million viewers.
In 2010, 9.4 million viewers tuned in to the first of three clashes between the then Conservative, Labour and Lib Dem leaders.
Broadcaster David Dimbleby, who hosted leaders' debates on the BBC in both 2010 and 2015, said a refusal to take part in TV showdowns with her rivals could be "rather perilous" for Mrs May.
"I don't think other parties will refuse to take part in debates, and I wonder whether Number 10 will stick with that, because it  may look a bit odd if other parties are facing audiences and making their case," he told BBC Radio 4's PM programme.
Theresa May will not take part in TV debates ahead of the planned general election, a Number 10 source says.