Gunners defender Holding ruptured his anterior cruciate ligament after coming together with Rashford in the 2-2 draw at Old Trafford.
But he insists there is no bad blood between himself and Rashford, only "love".
Holding, 23, shared a photo of the two of them going head to head and wrote alongside the image: "Marcus has reached out to me.
"We are just to (sic) Manc lads luckily (sic) enough to be against each other at OT.
"What happens after is just part of football. It's all love and my aim is to be back better than before."
Holding earlier showed how grateful he was for all the messages he had received.
The centre back, who joined Arsenal from Bolton in 2016, added: "This team is special! I love my guys. Thank you for all the support from players, staff and fans."
Holding has 16 appearances this season and looks to be in the good books of new boss Unai Emery, who said at the time that Holding had suffered a "big injury".
Holding's injury adds to Emery's problems, after a number of his players were shown inhaling 'hippy crack'.
Mesut Ozil, Pierre-Emerick Aubameyang and Alexandre Lacazette were among those filmed taking nitrous oxide at a wild party back in August.
But the Emirates boss has resisted punishing his players, with an Arsenal statement saying: "The players will be spoken to about this – and reminded of their responsibilities as representatives of the club."
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