Gibbs-White and Sanchez banged their heads together in Monday’s clash, leading to both men immediately dropping to the turf in agony.
The Forest midfielder had to be subbed off for Chris Wood in the 66th minute after taking a bad blow, as staff helped him off the pitch.
The injury has cast doubts over his availability for Thursday's Europa League semi-final second leg against Aston Villa, the most important game for the club so far this season.
After the game, Gibbs-White showed off his injury as he posted a picture of him olding a thumbs up as his caption read: “Thanks for the messages, what a win congrats T @awoniyi18.”
Forest extended their cushion to six points above the Premier League drop zone as they climbed away from fellow relegation candidates West Ham United and Tottenham.
They are now on a 10-match unbeaten run across all competitions ahead as their chances of going down to the Championship are lowered each week, especially as West Ham continue to drop points.
Forest are 1-0 up in their Europa League tie following Chris Wood's penalty at the City Ground in the first game and could book their place in the final if they hold their lead against Aston Villa on Thursday night.