Is it safe to get a thread lift the day after wisdom tooth is removed?

Because of the high risk of infection after your wisdom tooth surgery, completing a thread lift the day after is not recommended. I would either complete the thread lift a few days prior to the wisdom tooth procedure, or wait until you have completely recovered from the tooth extraction. We want to ensure your safety, so allowing for ample recovery time will minimize the risk of infection. Going forward, I would discuss your plans for wisdom tooth extraction with your board-certified expert to craft a treatment plan that works for your schedule. 

It is “safe” but not wise, depending on the area you are getting your thread lift. Thread lifts are done most commonly for the mid-lower face and neck which involves the area of the jaw where a wisdom tooth would be extracted. You can have swelling after a wisdom tooth extraction. I like to adjust the threads on each side to optimize symmetry. If your face is swollen I may not be able to assess and adjust as well.  However, if your thread lift is for your forehead or nose it may not be an issue. 
Another concern would be if there were any post op issues with wisdom tooth extraction. In the case that your oral surgeon needed to go back in after the procedure for any reason, it would reduce the efficacy of the thread lift by having to open your jaw for a long period of time. It is recommended that you not have dental procedures (anything requiring your mouth to be open for long periods of time) for one month after the thread lift of your lower face.
In summary, wait a good week after your oral surgery to get your thread lift. Hope this helps!