That incident was not officially reported, though the office was temporarily shut down.
The road near the Shwegondaing post office was cordoned off by police after Monday's explosion, witnesses said.
Although the military government frequently accuses its opponents of planning "terrorist" acts, bombings are relatively uncommon in Myanmar, formerly known as Burma.
In April last year, a series of six bombings in downtown Yangon caused minor damage but no injuries.
The government blamed opposition exile groups and ethnic minority rebels, who in turn suggested the acts were provocations by the military itself.