The 22-year-old singer took to Twitter to announce the disappointing news and apologise to fans just hours before the concert was slated to take place at the city's Alcatraz Club.
"I have Laryngitis. I'm so upset. I'm sorry to any fans in Milan tonight and to all who have travelled from abroad... I promise I will make it up to you," the 'Stay With Me' hitmaker wrote in a string of posts.
In another post, he told his followers that the cancelled show had been rescheduled for June.
Smith has been on the road to support his 2014 acclaimed debut album "In the Lonely Hour". The set, which peaked at No. 2 on Billboard 200, was among the contenders for Album of the Year Award at last month's Grammys.