At least four other soldiers in the Central Reserve Police Force (CRPF) were injured in the blast on Saturday, in the remote and impoverished Dantewada district, more than 400km south of the state capital, Raipur.
The blast occurred as the armoured truck in which the soldiers were travelling in rolled over an explosive device planted in the densely forested Bijapur area of the state, the independent Headlines Today television channel said.
Residents of a nearby village recovered the injured, including the commandant of the CRPF battalion, and at least 16 bodies from the badly mangled truck, the Press Trust of India (PTI) news agency said.
Police had reached the site of the blast and were trying to remove the remaining seven bodies still trapped in the truck, it said.
"The blast was powerful enough to lift the truck several feet in the air and split it into two," Ram Vichar Netam, the state's home minister, said on the television channel.
State chief minister Raman Singh said the bomb had been placed by Maoist rebels, PTI reported.
The communist rebels, who claim to be inspired by Chinese revolutionary Mao Zedong, have been fighting for more than three decades, demanding land and jobs for agricultural labourers and the poor.
They often target police and government officials, accusing them of colluding with landlords and rich farmers to exploit the impoverished.