The request was made at an urgent meeting at the Internal Security Operations Command (Isoc) chaired by Prime Minister Yingluck Shinawatra on Friday.
The army was asked to send 22 companies of soldiers to stand guard, a source at the meeting said.
Ms Yingluck voiced concern about the planned closure of 20 intersections in Bangkok on Jan 13.
The soldiers will be used to maintain security at the offices as there are not enough police officers.
About 20,000 police officers will be mobilised to oversee traffic that has been affected by the shutdown.
The source said the police and military will work together.
The security preparation for the shutdown came after military leaders objected to any invocation of the emergency decree by the government, saying there are no grounds for its enactment.
The decree would require troops to assist police in handling the shutdown situations. Soldiers standing guard at the offices don't require the invocation of the emergency decree.
At the Isoc meeting yesterday, armed forces leaders said they want the government and the protesters to launch a dialogue to defuse the political crisis.
The leaders said the dialogue would settle contentious issues, such as the design of national reform.