Fletcher's Notts team-mate and England bowler Jake Ball posted a picture of Fletcher with his thumbs up on Twitter, saying: "Horrible injury to @fletcherluke but looks like he's doing well #legend."
Nottinghamshire CCC chief executive Lisa Pursehouse has issued the following statement on the incident.
It reads: "Luke Fletcher has been taken to hospital to assess the extent of the head injury sustained in the NatWest T20 Blast between the Birmingham Bears and the Notts Outlaws and an update on his condition will be communicated in due course.
"He was able to walk off the field of play and, after receiving treatment from the medical staff, it was recommended he go to hospital for a thorough check-up.
Cricket is particularly sensitive to head injuries since the terrible accident that led to the death of Australia's Philip Hughes when he was struck on the back of the head batting for South Australia against New South Wales in Sydney in 2014.
"Nottinghamshire County Cricket Club would like to thank Sky, the ECB, the Birmingham Bears staff and the Edgbaston crowd for the sympathy and understanding they showed in an extremely difficult situation.
"The heartfelt round of applause given to the team as they left the field before returning was very much appreciated by the players and management."
Fletcher thanked fans for their support and tweeted: "Thanks for the messages. Shame about the result.
"Congrats to the bears!! Time for a few paracetamol."
Fletcher's team-mate Brendan Taylor tweeted: "Really worried for our mate @fletcherluke feel sick with what has happened. Hope you ok mate x."
Play at Edgbaston re-commenced at 21.18 and no overs were lost.
Birmingham went on to win an incredible game by six wickets, with the game going down to the last ball.
Fletcher, 28, has spent the entirety of his career at Notts apart from brief loan spells at Surrey (2015) and Derbyshire (2016).