Win Ko Ko, 25, and his brothers-in-law Phoe Ni and Aung Zaw Htway, both 25, from Pyithayataung ward, started stabbing each other with knives after an argument over family affairs.
Win Ko Ko died on the spot and Phoe Ni was taken to a hospital to receive medical treatment as an in-house patient.
Police arrested Aung Zaw Htway and charged him with murder.
Although there was a rumour that religious violence had erupted in the town, no outbreaks occurred after the stabbings, according to Meikhtila township administrator Myo Hlaing.
The police have increased security in crowded places in the town.