Stimson told BBC Radio Kent: "His knee is in a bad way and he has a bad neck. He's going to be out for a couple of weeks.
"He's had a scan on his knee, we should get the results of that this week. He's also had X-rays on his neck. I'm praying it's just a couple of weeks because he's a big player for us.
"Until we get the scan results we have to wait and see. He's been a big part of it. He'll be missed."
Transfer-listed keeper Alan Julian stood in for Royce in Saturday's 2-1 defeat at Huddersfield and will be keen to build on an impressive performance at the Galpharm Stadium.