Can Having a Single Dental Implant Placed Cause TMJ

Yes, this process could contribute to TMJ problems or pain. I would guess though that it's not so much due to the implant and more so due to the change in the bite. #27 (the lower canine or "eyetooth") plays  a crucial part in how the bite operates. 

If the current dentists aren't making any progress, then visit a TMJ dentist. Some medications could still be necessary. She may also need the right type of a splint or night guard.

It will be important to consider these bite problems when the final crown on the dental implant is made. She may need more assessment of the alignment of her bite NOW, while the implant is healing, so that it can be properly aligned with the new crown on the implant.

Does your wife clench or grind her teeth?  You may not know, but it sounds like the issue.  If the pain is worse in the morning then she is clenching at night.  If the pain is worse at the end of the day, then she has a daytime habit.  Pain meds will not help as much as a night guard and muscle relaxants.  The extraction causes inflammation which then aggravates the muscle and when people clench, they continue to aggravate the muscle even more.