I'm not a lawyer, never have been. And this is not legal advice in any interpretation. You need to speak to an attorney to understand any legal ramifications this situation may present.
You need to contact the vendor to see if you can purchase a commercial license.
It's doubtful anyone here will know for certain.
If this were to somehow happen to me, I would rapidly move forward with a rework of the logo using a font that is licensed for commercial use. This would be my top priority and all other work would take a back seat. This needs to be complete absolutely as quickly as possible.
When the rework is complete, I would then contact the client explaining the problem, and then offering the solution immediately. So the client isn't waiting in anticipation hoping to avoid any legal problems.
Be aware, if the client has to spend money to recreate things with the existing logo on them - such and stationary, signage, etc. - they may want compensation for any such expenditures. Since, clearly, this issue has only arisen because of the lack of due diligence on your part.