The host wore a surgical mask and used sanitizer after shaking the presidential candidate’s hand.
However Clinton played along with the joke and laughed before insisting: "I'm not contagious. … Nothing like a little rest when your doctor tells you to and you don't do it."
The pair chatted about her recovery from the illness, and Fallon asked if her husband, Bill Clinton, was a good nurse.
She described the former American president as "very solicitous" and "very sweet,” but quickly added; "My dogs were great, too.”
The 68-year-old was also presented with a large paper bag from Fallon, who said it had been left in Donald Trump’s dressing room after he appeared on the show a few days before.
"Let's look. I mean, let's see what's in there," Clinton said.
They proceeded to pull out a heart-shaped frame with a photo of Vladimir Putin in it.
Clinton seized the opportunity to mock Trump for his continued praise of him, calling their relationship, “the most famous bromance going."
"Besides me and [Justin] Timberlake," Fallon joked, making reference to his close relationship with the pop star.
"But Justin's worthy of your attention," she responded. "Because, last I checked, he hadn't killed off his adversaries."
Also in the bag was a Pink Floyd The Wall CD and a bag of softballs.
"That's as close as he's going to get to the wall," Clinton said.
As for the gift of softballs, Fallon explained: "Oh no, that was my gift to him. That's what I gave him. I'll give them to you later in the evening."
The appearance marked Clinton’s third on the late night show.
Can't get enough of Us? Sign up now for the Us Weekly newsletter packed with the latest celeb news, hot pics and more!