The debate -- the first ever in Italy between a sitting prime minister and the head of the opposition -- will be hosted on Rai1, the flagship station of the state broadcaster.
Meloni, head of the Brothers of Italy party, has been in power since October 2022 as part of a coalition with other right-wing parties.
Partly in response to losing that year's election, Schlein was elected to lead the opposition centre-left Democratic Party (PD) in March 2023.
Both of them are at the top of their party's lists for the June 8-9 European elections.
Neither will take their seats in the European Parliament however with Meloni planning to stay on as prime minister and Schlein preferring to remain a member of the Italian chamber of deputies.
Recent polls put Brothers of Italy at 27 percent in the European vote and the PD at 20 percent.
Apart from both being the first women in their respective positions, the two are polar opposites.
Meloni, 46, is a skilled orator with a modest suburban background. Her party stresses Italy's Christian roots and has put the fight against immigration on top of its agenda.
Schlein, 39, who is in a couple with another woman, comes from an academic family and also has US and Swiss nationality. She is less comfortable with public speaking than her rival.
Meloni's party is running on a campaign slogan of "Italy is changing Europe" while Schlein has focused on problems with Italy's healthcare system.
Negotiations over organising the debate were arduous, both teams said.
Schlein has for months accused the right-wing governing coalition of interfering with coverage at Rai, which she says has become a "government megaphone".
Italian leaders have long been accused of meddling with Rai, but insiders say intrusions have become more pronounced under Meloni.
Rai journalists have told AFP that investigative reporters have been pushed aside, pro-government commentators promoted, and programmes critical of members of the government cancelled or watered-down.
"I have worked at Rai for 20 years but I have never felt such pressure or seen as much censorship," Enrica Agostini, a journalist at Rai News, told the Foreign Press Association in Rome.
Some Rai journalists held a 24-hour strike this week, though most programming continued as usual thanks to a union more favourable to the government not joining.
"TeleMeloni is the fruit of imagination of the left", Brothers of Italy said this week on X.
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