Does an embargo on a Civilisation stop trade routes with their team mates?

Solution 1:

I just got myself into the exact situation I describe. My team mate has been embargoed: all (food and production) trade routes between us have been cancelled and cannot be re-established.

So the answer is actually Yes.

Solution 2:

Embargo impacts all external/international trade routes. If you have ever been embargoed you can see that you are still capable of sending trade routes to your own cities for food/production/religion spread(pressure), but nowhere else.

Worth noting that embargo does not actually impact your ability to trade goods such as gpt/luxury or strategic resources.