The team-mates collided while attempting to take a catch during a T20 Blast game with Sussex on 14 June.
Both players are now "on the mend" although Henriques, 28, broke his jaw in three places and Burns, 24, required stitches after cuts near his left eye.
"I literally don't remember any of the collision," Burns told BBC London 94.9.
"The first thing I remember is waking up. The Sussex physio was holding my neck and the paramedic was over my face.
"I remember the ball going up and thinking 'I've probably got to put my foot down here to try and get there' and then I got there, and then I remember diving.
"Other than that, I remember the whole game and then waking up and seeing the paramedics."
The match was abandoned after ambulances took the players from the field and Burns thanked the "fantastic" emergency staff.
"The headaches have died down a bit now," Burns added. "I'm on the mend.
"The support from (director of cricket) Alec Stewart and the lads was a great response and, when I woke up, it was nice for me to see my old man.
"He (Henriques) is in good spirits. He came off slightly worse, with his jaw and his teeth, but he's on the mend and that's the important thing.
"I don't think we'll be forgetting each other for a while. I'm looking forward to having a beer with him when he's fully recovered."
Surrey batsman Rory Burns says he does not remember his on-field collision with Moises Henriques earlier this month which left them both in hospital.