Do not assume that you have to choose between the two options.
First explore the ideal scenario, and only if that fails, consider choices.
Communicate with the company (not the HR, but with the employee who interviewed you / was interested in you / your research), and explain to them, that while you really want to do the internship and the position is exactly what you're looking for, it would be ideal if they could wait for X months for you to start it. Work with your professor to find some arguments about why it would be risky to your PhD to undertake the internship.
Best case scenario they will tell you that you can finish the PhD (or be close to it), and then get the internship.
Another possibility is that they will not be able to guarantee you the position after a X months (3-6 is a commonly accepted waiting time for a new employee joining), but still this does not mean that you will not be able to get the internship.
Depending on your field, it may be time critical to start as soon as possible, or it can not matter too much (they can wait a year). In addition keep in mind that internships are effectively free labor for the company, meaning that it's unlikely that they would not extend the same offer in the future (unless the team/department gets disbanded for some reason). Finally, when getting new employees or potential employees, what matters most is mindset/personality fit with the team, if you have that, it's likely they can wait.
If it turns out that you cannot get an extension to the offer, you can think of the following:
How easy is it to get similar internships? Try to apply to some, or at least discuss it with other companies in the field. If the field is extremely niche, then it might be hard because there are too few companies, or easy because there are too few candidates. This will help you evaluate the opportunity cost.
What is your end goal? If it's academia, focus on the PhD. If it's research/knowledge and working in the industry is a happy opportunity to do that, then you have options.
Taking the internship and not completing the PhD, is this an acceptable outcome?
How easy is it to find a job in the field? Try to actually do a job search, contact people working in the industry (or use the network of your professor) or at the very least have a talk with a recruiter. If there is demand for people with your expertise, losing the internship is not a big deal, as a job is incomparably better than an internship.
Good luck, don't stress about it too much, but try to gather as much data as possible to make an educated decision, hindsight is 20-20.