All three players were forced off during the second half of their goalless draw against Middlesbrough on Wednesday night.
Beckford and Wellens have groin injuries while Johnson, who was making his first league start in over three years at the Riverside, is nursing a shoulder problem.
"We will have to assess them and see how they are for Saturday," said City boss Sven-Goran Eriksson.
"Beckford and Wellens could not run. Johnson has a shoulder problem. It is not his knee, which is a relief, but there was pain and he could not run."
David Nugent has resumed training after a month out with a hamstring injury and the striker could be included in the squad.