As the studio audience gave him a raucous welcome, he said briefly in Arabic: "Please sit down, I am a simple man who does not like to be fussed over."
Youssef, one of Egypt's most popular TV presenters, was interrogated earlier this year by prosecutors on accusations of blasphemy and insulting President Mohammed Morsi.
The move drew criticism from Washington and free speech advocates.
During the show, Stewart expressed admiration for Youssef.
"Satire is a settled law. If your regime is not strong enough to handle a joke, then you don't have a regime," he said.
"You have to be able to handle anything. A joke is a joke," he added.
Youssef was released on bail after being questioned and the TV channel he appears on was threatened with having its license revoked.
Criticising the moves, Stewart said: "A joke has never shot tear gas at a group of people in a park. It's just talk.
"What Bassem is doing ... is showing that satire can still be relevant, that it can carve out space in a country for people to express themselves. Because that's all democracy is."
A trained heart surgeon, Youssef rose to fame when his videoblogs mocking politics received hundreds of thousands of hits shortly after the 2011 uprising that toppled President Hosni Mubarak.
Unlike other TV presenters, Youssef uses satire to mock fiery comments made by ultra-conservative clerics and politicians, garnering him a legion of fans among the country's revolutionaries and liberals.