The Italian international has suffered an injury to his left knee, and will see a specialist in Wales on Friday to assess the problem.
Rovers still do not know how long the player is likely to be out for, but the club is hopeful that the problem is deep bruising, rather than anything more serious.
Bruising would keep Campese out for around a week, but more serious issues could obviously see him out for longer.
“It’s not a recurrence of an old injury, it’s the other knee,” Chester told the Hull Daily Mail.
“It was an innocuous incident in that he got bumped off a tackle and landed on the floor.
“He’ll miss this week and it’s too early to say how long he could be out for.
“We won’t know anything until we get a report back from the specialist on Friday evening.”
There was better news for Rovers, however, with hooker Shaun Lunt likely to make his return. Adam Walker could also play, while Graeme Horne is recovering more quickly than expected from his pectoral problem.
“Shaun trained really well on Wednesday,” Chester said.
“We kept him off his feet yesterday and he’ll be involved in the team run tomorrow.
“We’re confident he’ll be available on Sunday.
“Having Shaun available will be a big boost not just for the team but for the coaching staff too. Shaun will give us more options and we are a better team when he plays because he adds another dimension to the way we play.
“Graeme is back from his pectoral injury and the medical staff have done a great job getting him back quicker than we thought.
“Adam trained yesterday and tells me he wants to play. We will make a decision tomorrow.
“He got the all-clear on Wednesday night after a positive x-ray. If on Saturday he tells me he still wants to play, he’ll play.”