One that's really famous in that country and has a rabid fan base.

Kim Kardashian would be swamped by paparazzi and her fans would just be taking mobile phone pictures, but she's no where near peak MJ in popularity. She's just pretty surgery in nice clothes, very nice clothes, but it's harder to care about someone whose only talent is making themselves look good because they're rich enough to effectively be able to focus on just that as a career.

Some boyband of which there's increasingly less support for that kind of fan base in western countries, but J pop and K pop artists would be a much bigger deal in South Korea and Japan, so may expect similar reactions over there. It's been a while since a boyband in the UK was a force to be reckoned with due to a legion of screaming teenage girls adoring them. Take That in early 90s England had probably the most rabid fan base since The Beatles.

As another poster mentioned, the Internet has diversified our tastes too much for such a cultural monolith to occur again. Something more then human would be needed for such hysteria again. Maybe a Black Friday sale, but that's a completely different kind of thing and not a person.

Beyonce is popular, but she's not MJ big. No one really is. Maybe Trump, but that's more like a cult following and a swindle, plus he's globally speaking way more loathed then he ever was respected (he's also not an artist in the musical sense, unless there's some Kid Rock duet in the works).