The England international now faces a scan after he was seen limping down the Old Trafford tunnel
Rashford, who was among the scorers in an entertaining game at Old Trafford, was seen limping down the tunnel after being replaced by Anthony Martial in the 86th minute.
When asked about his condition, manager Ole Gunnar Solskjaer confirmed there was an issue that would need further investigation.
“His knee was bothering him so [he will have a] scan tomorrow and see where we are,” the Norwegian told BBC Sport.
Solskjaer also praised the spirit of his side after they fought back from going behind early on thanks to a goal from Mohamed Salah.
Mason Greenwood levelled before half-time when he latched onto a searching pass from Rashford, becoming the youngest Manchester United player to score against Liverpool since Wayne Rooney 16 years ago.
Greenwood then returned the favour at the start of the second half, with his through-ball teeing up Rashford to put United in front.
Salah’s second of the game brought Liverpool level once more but, with extra-time looming, substitute Bruno Fernandes smashed home a stunning free-kick with 12 minutes remaining to send United through to the fifth round.
“You know when you go a goal down the reaction of everyone was really good,” added Solskjaer. “We played some really good stuff, scored some good goals, we have to defend well against them and we managed to react well and of course towards the end there were some moments but we kept them away.
“Marcus has played up front, down the right and left and we felt if we could switch the ball early today we could attack them because Liverpool defend on the front foot so we have to be quick on the ball, we did that well.”
Solskjaer also revealed that Fernandes had practiced free kicks in training on Saturday despite being told he was not going to be in the starting XI.
“Great goal, good free kick. When you leave him out like I did today, he stayed about 45 minutes after training yesterday shooting free kicks so I was pretty confident he could score one if he got the chance,” said the Red Devils boss. “He’s never happy with me when I tell him to go inside after training when he’s playing the next day so he got some practice yesterday.”