Antagonism between the Shinawatras and the establishment has divided the country for the past decade.
"The conflict between the elite, or the royalist military establishment, and the Shinawatras is far from over," said Kan Yuenyong, an analyst at the Siam Intelligence Unit think-tank.
He said the military had to "tread carefully" or the case could become a catalyst for protests.
The military ousted Yingluck's government in May saying it had to step in to end violent protests by establishment supporters bent on ousting what they said was an administration riddled with corruption.
Critics denounced the rice scheme as a populist give-away to the Shinawatras' rural support base.
The finance minister said on Feb 24 rice stockpiles stood at 17.5 million tonnes and the estimated loss incurred by the scheme totalled $16.46 billion.
The military government is still struggling to offload rice stockpiled under the scheme.
Authorities have held five rice tenders since the military took power and have sold 1,177,983 tonnes for about 17 billion baht ($526 million).
Exporters criticised the subsidy for distorting the market and dethroning Thailand as the world's biggest rice exporter.
The junta has said it has no plan to revive rice subsidies.