Police said an investigation was under way but would not elaborate on whether there were any suspects in the attack.
Footage broadcast on Myanmar TV station DVB showed extensive damage internally and externally to a branch of Yoma Bank.
Yoma Bank said two of its Lashio branch employees were killed and that both of its branches in the city would be temporarily closed.
Lashio is in Myanmar’s restive Shan State where several ethnic insurgent groups are fighting the Myanmar military.
The two dead were both women, government spokesman Zaw Htay said in a post on Twitter linked to a government statement on the Lashio explosion.
The military said in a statement 22 people were injured.