Following her win, Dame Maggie addressed the US comedian in a statement posted on Twitter by Masterpiece PBS.
“I was very astonished and pleased to win the award,” she said. “I feel the Emmys have been overly generous to me.
“If Mr Kimmel could please direct me to the lost and found office I will try and be on the next flight.”
The message was signed off, “Love, Old Maggie”.
Dame Maggie was awarded the Emmy for best supporting actress in a drama series for her role as Violet Crawley, Dowager Countess of Grantham, in Downton Abbey. It was the third time she has received the award for her role in the hit period drama.
Her rivals in the category included Game Of Thrones stars Lena Headey, Emilia Clarke and Maisie Williams.
During his opening monologue, Jimmy joked that Dame Maggie should have made an effort to be at the event, having not attended in previous years either.
“If you want an Emmy you better hop on a plane right now and get your Dowager Count-ass over here,” he said.
“When her name was announced as winner, he walked on to the stage to take Dame Maggie’s trophy, saying: “No, no, no, no, no. We’re not mailing this to her. Maggie, if you want this, it’ll be in the lost and found.”
The final episode of Downton Abbey was broadcast earlier this year after six series.