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human
PhD Advisor Doesn't Let His Student Go on Internships

Okay, I recently got an internship and I need to file my paperwork which requires the approval of my advisor. Here is some background about me and my lab:

I am an international student in an US university and I started my Ph.D. in Fall 2018 and have passed my qualifiers and published a journal paper and am writing my second paper currently. I don't intend to stay in academia after graduating, and I have no work experience hence I applied for an Internship to get jobs after I graduate. It is difficult to get jobs in the US when you have no work experience and are on a visa.

Now my advisor is known for not allowing his students to go on internships. Two of my colleagues in my lab couldn't go on internships as my advisor strongly advised them not to and some of his former students didn't even apply. My relationship with my advisor is positive so far however, I am concerned as to how I can approach him about this. I will send him an email explaining my situation sometime this week as I need to keep the company informed too.

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I would like to get your input on how I should go about approaching my advisor. How I should react in case he says no.  What should I say and what should I avoid.  Thank you very much for your advice.

Clarification: before joining the lab I have informed my advisor that I will work in the industry and not academia. Furthermore, the funding in the lab runs out before summer and there is no incoming source of money as far as I know.

Thank you all for the responses. I appreciate them greatly.

Update: So, I spoke to my advisor,  yesterday and in short he agreed to the internship under the condition that I keep working on our research. He shared his concerns with me, as about 5-6 years ago he had 2 students who did excellent work for him went on interns, one did not come back and the other came back only to graduate within a semester and did not pursue any more research work. I reassured him of my intention to return to the program, and that legally I cannot just take a full-time job after my intern is over as my visa won't allow me to just quit my program and start working for any company in the US. He agreed the intern will significantly help in my personal career growth and will save him some money as he won't have to pay stipend over the summer. While I would have preferred to work the internship alone in the summer, however, getting the research work done will be beneficial to me in the long run. He further emphasized the need to be in a strong position to graduate, by working in the summer and producing more paper I will be in a safe position and can graduate quickly in case he is unable to get funding. I agreed with his reasoning, I do want to finish my degree and achieve my research objectives without having to support myself. 

Again thank you all for the kind and supportive advice you provided to me in handling this delicate situation.
gpt
It’s pretty early in the year - if you have a good working relationship w him perhaps ask him to go for coffee and ‘advice’ - explain the situation (many US faculty don’t know all the visa rules that international students deal with), and that you have been advised that this would help you post- degree, ‘but you don’t want to leave the lab short staffed for 10 weeks this summer’ — so is there a way to get work done in the spring (etc etc) 
In your conversation project a belief that you both want the best for the lab *and* for you / your future - and that you need help figuring out how to do this.