Rivers then said that Adele was very scared because she sang at the awards.
She said, "My throat, my throat! I don't know if I can swallow. And I said, Oh yeah, you can swallow," she added.
This is not the first time that Rivers has made a joke at Adele's expense.
On Oscars night, she had tweeted that on Sunday night, people could easily pick Adele's Oscar statuette out of a lineup as it was the only one that was wearing Spanx.
And when Adele gave birth to her son, Angelo James, in October, Rivers tweeted, "Congratulations to Adele on the birth of her 68 pound 8 ounces bouncing baby boy."