That sees Worcester flanker Kvesic, who has been in superb form for the Warriors this season, join up with the England senior squad for the first time in his career ahead of the upcoming RBS 6 Nations campaign.
"I have been fortunate to have a run of games at Warriors, and now I am delighted to get the call from England," Kvesic said.
"It would be fantastic to get the opportunity to feature in the Six Nations, but my priority now is meeting up with the team, keeping my head down and working hard to try and make that a reality."
Chiefs head coach Rob Baxter, speaking immediately after his side's Pool 3 defeat to Leinster refused to rule Johnson's out of the start of the international campaign.
"He's done something to his knee and his ankle but until we get it scanned we're not going to know how serious it is," he said.
Elsewhere in the forwards, Calum Clark has picked up a shoulder injury and that means Saracens lock Mouritz Botha has been included as a precaution.
Clark's director of rugby at Northampton, Jim Mallinder, admitted he feared the worst after the 23-year-old was forced off in his side's defeat to Glasgow Warriors.
"The medics will take a good look at Calum's shoulder but it does not look good and I think he could be out for a while," he said.
Harlequins wing Ugo Monye will also train with the squad while players involved in games over the weekend are assessed.
That group includes Gloucester fly-half Freddie Burns, who went off nursing a knee problem during his club's Amlin Challenge Cup victory over Mont-de-Marsan on Saturday.