The crew from Bracknell were called to the first floor flat in Hanover Gardens, Hanworth, at 5am this morning (Sunday).
Watch manager Michael Fulwell said: "She had just been looking for something and caught her hand between the seat and the arm.
"The chair had a wire frame and she got her hand in, but couldn't get it out."
Firefighters got her hand out in 10 minutes.
It is not known how long she was stuck for.