The "Stay With Me" singer's team on Wednesday announced that Smith would be cancelling his upcoming performances in Azerbaijan and at the 2019 Billboard Music Awards via a statement posted on his Twitter account, reports people.com.
The note read: "In the wake of cutting his South African tour short last week, Sam's medical specialists are requiring him to have further rest.
"Regrettably this means that he will be unable to perform at the Azerbaijan Gran Prix in Baku this weekend or the Billboard Music Awards in Las Vegas next week. We apologise for the disappointment for those affected, but the primary focus at this time needs to be on Sam's recovery and health."
As reported last week, Smith stopped his first-ever Cape Town concert just 45 minutes after it started due to vocal strain.
This is not the first time Smith has run into vocal troubles. In May 2015, he underwent surgery to stop recurrent vocal cord haemorrhage (bleeding).
At the time, Massachusetts General Hospital - where Smith was operated on - explained in a statement that "this condition is the result of unstable blood vessels in the vocal cord that can rupture and prevent vocal performance".