The Robins medical staff had feared that the midfielder had suffered a fractured forearm during a collision in Tuesday night's 1-1 draw with Leicester.
However, following X-rays on Wednesday, club physio Nick Dawes told the club's official website: "Cole has got the all-clear which is great news.
"He's still quite sore but hopefully he'll be available for selection for Sunday's game."
Johnson will be without striker Alvaro Saborio, who has returned to his native Costa Ricafollowing an unsuccessful loan spell at the club.
Jamie McAllister (calf) and Jamal Campbell-Ryce (calf) remain sidelined.
The match kicks off at 2pm.