The pair collided while attempting to take a catch during Sunday's T20 Blast game with Sussex at Arundel.
The match was abandoned after ambulances took them from the field.
Australia international Henriques, 28, broke his jaw in three places, while Burns, 24, had cuts around his left eye that required stitches.
Surrey announced on Twitter on Monday that the pair were "in decent shape".
And a further update from the club on Twitter 24 hours later read: "More good news on the lads - Moises has now been released from hospital and will see a dental specialist tomorrow. He's improving slowly!"
Burns, meanwhile, tweeted his thanks "to all the medical staff" who treated the pair and his hope that his club colleague "keeps progressing well."
Team-mate Kevin Pietersen, who was in the field at the time of the collision, said the incident deeply affected the team.
"I kept thinking one of the guys will call. Then you think one will stop but then bang, bang. It was absolutely sickening," Pietersen told the Daily Telegraph.
"When those guys went down and did not move it hit some of our guys very hard.
"It was the right decision to abandon the match. We had lost two of our players, a lot of players were crying in the dressing room and it is only a game of cricket."
Director of cricket Alec Stewart also posted a picture on Twitter of Burns smiling in his hospital bed.
Henriques, who has played three Tests, six one-day internationals and four T20 games for Australia, joined Surrey in April as an overseas player for their T20 Blast campaign.
Surrey-born Burns, a left-handed batsman and occasional wicketkeeper, made his first-class debut for the county in 2012.
Surrey's County Championship game with Glamorgan began as scheduled on Monday.
Moises Henriques has been released from hospital following the on-field collision with Surrey team-mate Rory Burns that left him with a broken jaw.