OP I would say that his dad was having a difficult time emotionally. He's not ill but he needs time to himself and and no-one knows how much time but he will definitely not be seeing him for probably a long time.
Tell him it's not anything that he did, or said, or didn't do or say it is just something that happens sometimes and adults can find it very difficult to cope with. Reassure him that you're not going anywhere. Say something like, lucky for me I've had a check up and I'm fine, or something child friendly that he will understand.
Would it be possible for him to write letters to his dad which you could forward via his family? Does he have a photograph of him?
I would say that it's really impotant to tell his school because they can keep an extra eye on him and give him support if he needs it. He is likely to talk about it to staff (these things have a habit of just popping out) and it will be better for him to do that rather than holding it inside.
Also, ask the school if they have any nuture groups, emotional literacy support workers or any other way that they could help him come to terms with what is, essentially, grief at the loss of a loved one.
I wouldn't tell him during the holidays as someone suggested because school is part of his daily routine, it's a safe environment where he will feel comfortable and where you can access more support for him. But booking a trip for a few weeks ahead might give him something to look forward to and focus on.