A statement announcing the decision on behalf of President Thein Sein was broadcast on state television.
Thein Sein said that the move would enable the military to help restore order in the riot-hit town, south of Mandalay.
At least 20 people are reported to have been killed since the violence began, but exact figures are unclear.
Meiktila MP Win Thein said scores of mostly Buddhist people accused of being involved in the violence had been arrested by police.
He said that he saw the bodies of eight people who had been killed in violence in the town on Friday morning.
The disturbances began on Wednesday when an argument in a gold shop escalated quickly, with mobs setting mainly Muslim buildings alight, including some mosques.
Fighting in the streets between men from rival communities later broke out.
Meanwhile people in Meiktila said they are affected by food shortages because the main market in the town has been closed for the last five days.
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