The champion jump jockey suffered the break in a fall from Westend Story at the sixth fence in the Dare To Dream Novices' Limited Handicap Chase.
Trainer Philip Hobbs, for whom Johnson is stable jockey, later confirmed the extent of the injury.
Johnson was assessed in an Exeter hospital - and after speaking to him, Hobbs said: "He has broken his right arm in between the elbow and the hand.
"He is going to have an operation on it, to have it plated, either tomorrow or Thursday.
"He expects to be off for a month or so. He sounded very positive about Cheltenham."
Johnson, champion jockey in each of the last four seasons, trails Brian Hughes by three winners in their title battle.
This year's Cheltenham Festival is due to get under way on March 10.
According to information on the Professional Jockeys' Association website, Johnson's recovery may be on a tight timeline - with the average absence from race-riding because of a broken arm almost nine weeks.
Hobbs' top novice hurdler Thyme Hill is among Johnson's big Festival hopes - while Tom O'Brien took over his two remaining rides for the stable at Exeter, following his misfortune on 11-8 favourite Westend Story.
Major bookmakers immediately suspended betting on the title race when it was reported Johnson had suffered a potentially significant injury.
