This will work for all window panes not just the NERDTree pane. These lines go above.

set cursorline 
set cursorcolumn

These lines go below.

augroup cursor_off
    autocmd!
    autocmd WinLeave * set nocursorline nocursorcolumn
    autocmd WinEnter * set cursorline cursorcolumn
augroup END

This will work for all window panes not just the NERDTree pane. These lines go above in your .vimrc.

set cursorline 
set cursorcolumn

These lines go below in your .vimrc.

augroup cursor_off
    autocmd!
    autocmd WinLeave * set nocursorline nocursorcolumn
    autocmd WinEnter * set cursorline cursorcolumn
augroup END