McKinnell said Labour was heading down an "increasingly negative path" amid "internal conflict" stemming from the recent shadow cabinet reshuffle.
"As somebody who came into politics with the sole motivation of making life better for my city, my region and, by extension, the country as a whole, I recognised that our electoral defeats in both 2010 and 2015 demanded a genuine and profound response from the Labour Party," she wrote in her resignation letter.
"I feel that I would like to channel my energy constructively, into making positive changes for my constituents," she added.
She is the fourth MP to quit the front bench since Corbyn's reshuffle.
Last week's reshuffle saw the exit of shadow Europe minister Pat McFadden and former shadow culture secretary Michael Dugher and the demotion of shadow defence secretary Maria Eagle to culture spokesperson.
Speaking on the BBC earlier, Corbyn defended the changes he made to the shadow cabinet, saying they had brought more "diversity" into his top team and he was "happy" with the new line-up.
"We have a team which is strong. We have widened the shadow cabinet to represent the diversity of the country and the membership of the Parliamentary Labour Party. I am happy with it. We are moving on," he said.
