Sheeran badly injured himself after falling from his bike in mid-October.
The 'Perfect' singer's doctor has told him that with physical therapy he should be back performing early next month in Singapore.
However, he has had to cancel shows in Taipei, Hong Kong, Seoul and Jakarta.
"I haven't canceled a show before, this has been quite a difficult decision to do but I physically can't play at the moment and it's the utmost importance to get my arms healed so I can play hopefully for the rest of my life," he said in a video shared on Facebook.
The 26-year-old continued to apologise to his fans, "I'm sorry for everyone affected and I hope you understand my reasons for doing this."
With Sheeran returning to the stage next month, this means that he will still be performing in Australia next year.