The "Shape of You" singer is due to perform in Mumbai on November 19 as part of his Asia tour which starts from November 11.
The tour dates in Singapore, Kuala Lumpur, Bangkok, and Dubai will also go ahead as scheduled, according to a statement on Sheeran's official website.
Sheeran has rescheduled his tour dates with Osaka, Tokyo and Manila to April 2018, and cancelled his shows in Taipei, Seoul, Hong Kong and Jakarta.
The singer had posted on Instagram a photo of a plaster cast on his lower right arm.
"Ive had a bit of a bicycle accident and I'm currently waiting on some medical advice, which may affect some of my upcoming shows. Please stay tuned for further news," Sheeran had said.