Owen, who has just suffered another injury setback with a hamstring problem that will keep him out of action for several weeks, said Hernandez should not take his success for granted.
Owen told BBC Radio Five: "It's obviously early days for him but he's made a really good impression at the club, scored goals in the last couple of games.
"He's young, sharp and a good finisher. He seems to be thriving, he's always got a smile on his face, he enjoys his football and the fans have taken to him already.
"So far so good, but, as I know, football changes in a week or whatever.
"Hopefully it's the start of something good for him, but he needs to keep working hard and keep putting in those performances because at Man United that's what it demands - you score one week, but if you play poorly the next week then you could be out the team so you need to always be on top of your game.
"Thankfully he's playing well at the minute, and long may that continue."