I'm surprised no one bothered to ask if there's a backup of any type before malware was detected.
That said, I would give https://sucuri.net/website-antivirus/signup a try for a clean up. That is pretty much the only thing left before a wipe and reinstall.
Without any previous backup, backing up current state would not fix it. You can try and delete everything but "/wp-content/themes/" .... Make a note of your plugins.
Another thing I would try is optimize, analyze and clean up your database tables. In PHPMyAdmin there's an option for that with just a click. Might help.
Then after all that, give it a try and see if the malware is gone. It's pretty much an approach compare to losing it all, deleting your tables, etc..
Hope that works. Keep us posted on how things work out and what works or what you ended up doing in the end for others that might find this thread looking for help :)