The Dane revealed the news on Twitter, posting: "Broke my hand after falling off my bicycle. Better stick to four wheels."
Earlier in the day, the youngster had revealed he wouldn't be in Singapore for this year's race, and posted a picture from last year when he contested the race, going on to finish tenth..
"Kevin has been training extensively on his bicycle over the past few weeks and months, but unfortunately he fell off it the other day," a McLaren spokesman confirmed. "He has sustained a small fracture in his left hand, but is expected to make a full recovery within the next three weeks or so."