It should be possible. I think I know how but this is as hacky as it gets. You will need Virtual Audio Cable:
http://software.muzychenko.net/eng/vac.htm it is not free though.
You will have an extra device in your playback and recording devices. Those are connected with each other and are to be considered the same device. Which means when you feed something into the recording VAC device, it will output it from the playback VAC device.
You will need to forward your default playback device to the recording VAC device(tools for this are included with VAC), then you configure your music player to use the VAC playback device instead of your default playback device.
Then you select the VAC recording device as your microphone in the OBS setting. Next, mute the audio in OBS as you will play all the sound from the microphone device. You should be done now.
Oh, and if you want to talk to the viewers, you will need to forward your microphone to the VAC recording device as well.
This method is not guaranteed to work, but I have tested a similar setup in Xsplit.
Note that this method will cause a slight sound delay.