Добавляем в /etc/nginx/sites-available/default в секцию server{}:

	location /phpmyadmin {
	    root /usr/share/;
	    index index.php index.html index.htm;
	    location ~ ^/phpmyadmin/(.+\.php)$ {
		    try_files $uri =404;
		    root /usr/share/;
		    fastcgi_pass unix:/run/php/php7.0-fpm.sock;
		    fastcgi_index index.php;
		    fastcgi_param SCRIPT_FILENAME $request_filename;
		    include /etc/nginx/fastcgi_params;
		}
	    location ~* ^/phpmyadmin/(.+\.(jpg|jpeg|gif|css|png|js|ico|html|xml|txt))$ {
		    root /usr/share/;
	    }
	}
	location /phpMyAdmin {
	    rewrite ^/* /phpmyadmin last;
	}

Перегружаем nginx:

sudo service nginx reload

В Ubuntu 16.06 ошибка:

The mbstring extension is missing. Please check your PHP configuration

Доустанавливаем:

sudo apt-get install php-mbstring php7.0-mbstring php-gettext
sudo phpenmod mcrypt
sudo phpenmod mbstring
sudo service apache2 restart

http://askubuntu.com/questions/772397/mbstring-is-missing-for-phpmyadmin-in-ubuntu-16-04

#1698 - Access denied for user 'root'@'localhost'

По умолчанию root в базе создан на аутентификацию из системы:

GRANT ALL PRIVILEGES ON *.* TO 'root'@'localhost' IDENTIFIED via unix_socket;

Необходимо поменять на:

GRANT ALL PRIVILEGES ON *.* TO 'root'@'localhost' IDENTIFIED BY 'пароль';
FLUSH PRIVILEGES;