Ruby Mart was seen ablaze at around 2 a.m. local time on Thursday (1930GMT on Wednesday), with some onlookers capturing images of the fire on their phones.
Local media said two military-owned malls were on fire on Thursday morning during a curfew, with two people arrested near Ruby Mart.
Myanmar has been rocked by almost daily protests since the army overthrew Aung San Suu Kyi's elected government on Feb. 1 citing unsubstantiated claims of fraud in a November election. Suu Kyi and other members of her National League for Democracy (NLD)
are being held in detention.