Music can be played only if you are sharing your screen.
Create a presentation with just one slide – show the title of the meeting or show Break.
Run the presentation.
Choose Share button – choose the running presentation window
Enable the Include system audio button
Mute your microphone
Play music from your PC.
When you want to speak, unmute yourself and stop the music.
You need to use a Sound Mixer to route system playing sound to your mic.
Two options: software mixer like VBCable or hardware mixers like Rodecaster Pro, Zoom, ProSonus, etc.
The mixer allows you to combine the microphone sound along with music or sound effects.
Now, on the mixer, mute the mic and play music.
Choose the mixer device as the audio microphone input in Teams.
Set the Teams Noise Cancellation to Low or Off.
If Teams Noise Cancellation is High, the music will be distorted. 
In Teams meeting, unmute the mic.
Now the audience will hear the music.
When you want to talk, unmute yourself on the mixer and stop music playback.
You must have two devices. For example, desktop PC and mobile.
Use one device to join the Teams meeting and the other device to play music.
Let us say, we connect to Teams meeting using a laptop.
Use the default microphone.
Keep the microphone on mute.
Set the Teams Noise Cancellation to Low or Off.
If Teams Noise Cancellation is High, the music will be distorted.
Now play music on the mobile phone (or another device).
Unmute the mic in Teams.
Now, music will be heard by the meeting attendees.
Warning: Any other sound, noise or your speech will also be heard by the audience.
In short, anything that the laptop mic can hear will be heard by attendees.
If you do not want people to hear your voice but hear the audio, then you need the mixer.
See the previous question.
2 Responses
I want to play media on chrome while still being in the meeting on MS Teams. I do not want to share the sound or screen with anyone. Only I should be able to listen to that sound. But while the meeting is on no media sound is audible. Please help.
By default, whatever you are playing on the PC does not get transmitted to meeting participants. Even when you share the screen, you have an option to share the locally running audio. By default it is OFF.
However, if you are playing music on the PC, the microphone may pick up some of it and others may hear it.
Nowadays, due to built-in noise cancellation, the music may be cancelled automatically.
If you want to be fully sure of no music leakage to the meeting participants, the simplest option is to use headphones.