Should I report to my supervisor if 1 of my team mate is not doing his work? Or would that mean I'm not a good team member?

Yes and no. But basically no if you and other team members can sort the problem within the team.

Escalating matters should be done if they’re above your pay grade or you want to raise issues to your direct manager that you know you can’t handle yourself.

Think about it. Nobody likes a tattle tale.

In a team, everyone should be pulling their weight. It isn't fair for a few members to carry the rest. If you're worried about getting your team mate into trouble, you might speak to them first to see if you can help them overcome any blockers. It could be something easily resolved.

If they're finding the work too challenging generally, or they're having issues in their personal life that are interfering with work, they need to speak to the supervisor.

I think we need more details here. Is that team member not doing tasks assigned to them, or ones they could accomplish? Are they using the time not spent actively working in some other productive way? Are they simply slow, or are they taking a lot of breaks? Are they balancing out with overtime? Are they a junior developer?

This can be a motivational issue. It can also be a work-break balance thing. It can be laziness or they're keeping themselves free for urgent issues/pair programming.

What workflow are you using? This could also simply be a matter of setting personal targets and achieving them - perhaps a mismatch with the overall project targets.

Them not doing their work isn't your problem.

Them causing problems for work is your problem.

Talk to your supervisor about the problems you actually have. :)

You should to speak and ask why he isn't working... sometimes not good member have a lot problem like motivation or mental, the first key of team is speak...